In simple terms, he is referring to monopolization.
The essential conditions for the existence and for the sway of the bourgeois class is the formation and augmentation of capital; the condition for capital is wage-labour. Wage-labour rests exclusively on competition between the labourers.
Here Marx is saying that the bourgeoisie need capital, capital needs wage labor, and wage labor needs competition. The foundations of all of capitalism is thus competition. If competition ceased to exist, then wage labor would cease to exist, then capital would cease to be useful for the bourgeoisie, and then the bourgeoisie as a class would collapse.
The advance of industry, whose involuntary promoter is the
bourgeoisie, replaces the isolation of the labourers, due to
competition, by the revolutionary combination, due to association.
It becomes obvious here from this perspective that this paragraph is referring to the destruction of competition, i.e., monopolization in simple terms. This concept is crucial to Marx's economic theories, and is something he develops much further in Capital.
Marx was building on economists before him. Adam Smith wrote,
The owner of the stock which employs a great number
of labourers, necessarily endeavours, for his own advantage, to make
such a proper division and distribution of employment that they may be
enabled to produce the greatest quantity of work possible. For the
same reason, he endeavours to supply them with the best machinery
which either he or they can think of. What takes place among the
labourers in a particular workhouse takes place, for the same reason,
among those of a great society. The greater their number, the more
they naturally divide themselves into different classes and
subdivisions of employment. More heads are occupied in inventing the
most proper machinery for executing the work of each, and it is,
therefore, more likely to be invented.
Adam Smith argued that capitalists (employers/business owners) in a competitive market would want to reduce labor time as much as possible, they would much rather their workers produce, let's say, 10 cellphones an hour than 1 cellphone an hour. This is known as worker productivity, and capitalists would strive to make their workers as productive as possible. Thus, it is in the capitalist's interests to innovate, to invest in new technology and machinery, and to invest in research.
Marx agrees with Smith that capitalists would want to innovate. Fundamentally, the reason employers innovate it to cheapen the price of commodities. If they can produce the commodity cheaper than their competition, they can undercut them, so they want to make the production process as productive as possible.
The battle of competition is fought by cheapening of commodities. The
cheapness of commodities demands, caeteris paribus, on the
productiveness of labour, and this again on the scale of production.
Therefore, the larger capitals beat the smaller.
The problem with this that Marx points out is that this inherently means that larger capitals defeat smaller capitals, large businesses crush small businesses. Most people know someone who has complained about Walmart coming into the town and bankrupting all their local grocery stores. It's just inevitable since that's the reason capitalists innovate in the first place.
It will further be remembered that, with the development of the
capitalist mode of production, there is an increase in the minimum
amount of individual capital necessary to carry on a business under
its normal conditions. The smaller capitals, therefore, crowd into
spheres of production which Modern Industry has only sporadically or
incompletely got hold of. Here competition rages in direct proportion
to the number, and in inverse proportion to the magnitudes, of the
antagonistic capitals. It always ends in the ruin of many small
capitalists, whose capitals partly pass into the hands of their
conquerors, partly vanish.
Here Marx points out one of main reasons why small businesses cannot compete with large ones. As large businesses industrialize and become more and more technologically advanced, the cost of operating a business at that scale becomes ever so larger, and the cost of investing in that new technology, the barrier of entry for new businesses, becomes ever so larger.
Therefore, small businesses, or new start-ups, simply do not have the wealth necessary to compete. Most will go bankrupt, or they will move to some part of the economy that is currently underdeveloped and still has competition, but it is only a matter of time before these large enterprises find a way to move into those economic sectors as well.
We see then what Marx means in the Manifesto when he later goes onto say this:
The development of Modern Industry, therefore, cuts from under its
feet the very foundation on which the bourgeoisie produces and
appropriates products. What the bourgeoisie therefore produces, above
all, are its own grave-diggers.
Capitalists will tell you the reason capitalism is great is because it is great at "innovating". The point Marx is making here is that this very innovation, the very act of developing industry, inevitably destroys capitalism over time, because the bourgeoisie, that is, the owners of industry, can only make wealth off of capital if they have wage labor, but wage labor can only exist with competition, and the development of industry destroys competition.
Vladimir Lenin in the first chapter of Imperialism, the Highest Stage of Capitalism goes into detail using economic data to demonstrate how this process is occurring in real life, and he summarizes it as such:
Competition becomes transformed into monopoly. The result is immense
progress in the socialisation of production. In particular, the
process of technical invention and improvement becomes socialised.
This is something quite different from the old free competition
between manufacturers, scattered and out of touch with one another,
and producing for an unknown market...Capitalism in its imperialist stage leads directly to the
most comprehensive socialisation of production; it, so to speak, drags
the capitalists, against their will and consciousness, into some sort
of a new social order, a transitional one from complete free
competition to complete socialisation.
In summary, the development industry takes workers out of isolation from one another and puts them into association with one another.
Friedrich Engels uses similar language to this in The Principles of Communism
What will this new social order have to be like? Above all, it will
have to take the control of industry and of all branches of production
out of the hands of mutually competing individuals, and instead
institute a system in which all these branches of production are
operated by society as a whole – that is, for the common account,
according to a common plan, and with the participation of all members
of society. It will, in other words, abolish competition and replace
it with association.
What Engels is saying here is that in a post-capitalist, socialist society, competition would be replaced by association. You would no longer have competition between individual economic firms, rather, all workers would work in cooperation with each other according to an nationwide economic plan.
When Marx and Engels criticized capitalism, their criticism of capitalism is not that capitalism is morally bad. In fact, they criticized those who said as much. As Engels writes in Socialism: Utopian and Scientific:
The Socialism of earlier days certainly criticized the existing
capitalistic mode of production and its consequences. But it could not
explain them, and, therefore, could not get the mastery of them. It
could only simply reject them as bad. The more strongly this earlier
Socialism denounced the exploitations of the working-class, inevitable
under Capitalism, the less able was it clearly to show in what this
exploitation consisted and how it arose. but for this it was necessary
What Marx and Engels are trying to point out here in the Manifesto is not that capitalism will fall because capitalism is "bad", but that capitalism will fall because capitalism's foundations are built upon competition, and capitalism itself reshapes the material conditions of the economy over time such that competition is no longer possible.
Therefore, the inevitable conclusion is that capitalism must collapse, and into its place will be a new economic system which favors these new conditions, and this new economic system is socialism.