Democritus was a student of Leucippus of Miletus, with whom the (or 'an') atomic theory appears to have originated. In the background, too, was the Eleactic School of Parmenides and Zeno, with which Leucippus was almost certainly acquainted and against which Demoocritus reacted.
For Parmenides the world of Being, the world that truly is, is self-existent, indivisible, uncreated, eternal unmoved and unchanging.
For Zeno, there is infinite divisibility, no end to the division of a section into parts.
While both Parmenides and Zeno believed much more than this, these are the points of relevance to Democritus' atomism.
Democritus was convinced that there is change and movement in nature. If there is movement there must be a medium in which movement takes place. Bodies or material things cannot move unless there is 'the empty' in which they can move. Hence the Democritean Void.
Democritus was also unwilling to apply Zeno's infinite mathematical division to the material or physical world. There may be an infinite number of points between any two points but physical division is different from mathematical division. Democritus points back in agreement with Leucippus : 'The atomists hold that splitting stops when it reaches indivisible particles and does not go on infinitely' (quoted in S. Sambursky, 'The Physical World of the Greeks', London : Routledge, 1963, p. 107).
Democritus's 'atoms' are 'ta atoma (somata), 'the uncuttable bodies' (J. Barnes, 'The Presocratic Philosophers', London : Routledge, 2nd ed., 1982, 344). I think his basic idea was that you can take a material and physical body and 'cut' or divide it and carry on doing this but that there is a lower limit to the division of matter otherwise you would reach a dimensionless point which could not count as material or physical at all. The lower limit is that of the atoms.
I think he merely hypothesised that changes and movements were due to the different shapes, arrangements and positions of atoms in the Void. Also, that the innumerable atoms in the Void bring objects into existence when they unite and destroy them when they separate.
Why the atoms should move, and thus produce changes in the objects they constitute, Democritus does not tell us. The atoms exist, have always existed, in a swirl : this is a matter of necessity or fate for which no explanation can be given.
Democritus has not been neglected. He was largely unavailable. It was only in the late-19th and early 20th centuries that the Presocratic fragments - which is all we have for nearly all of the Presocratics - were systematically collected, arranged and published by H.A. Diels. (His work was continued and revised by W. Kranz.) Marx, we might recall, wrote his doctoral dissertation on the material available to him : 'The Difference Between the Democritean and Epicurean Philosophy of Nature' (1841).