I've read on many websites (including Wikipedia) that empiricism is the opposite of innatism. Could someone explain me why?
There's not much in this question that can't be answered by direct reference to the core definitions of the two terms:
Empiricism: The theory that all knowledge is derived from sense-experience. (Google)
Innatism: A philosophical doctrine that holds that the mind is born with ideas/knowledge. (Wikipedia)
If the mind comes into the world with knowledge, then presumably that knowledge is not derived from sense-experience.
Anyone who simply says 'empiricism is ...' or 'innatism is ...' is bound to run into the criticism that both terms are many-ways ambiguous. But at the level at which I assume you are asking the question, I'll venture a characterisation of the difference.
Empiricism on a standard view is an epistemology, a theory of knowledge, on which all knowledge derives ultimately from experience. I have no knowledge of anything until I have some experience of it or relating to it. Innatism by contrast is very roughly the view that all knowledge does not derive ultimately from experience but that we have ideas (concepts or principles : they could be the idea of God or the rules of deductive logic for example) which we are born with and do not learn from experience.
Most textbooks cite Locke in the 17th century and Berkeley and Hume in the 18th as the leading 'modern' empiricists though the label can be contested. Locke is known, however, for an extended discussion and 'refutation' of innate ideas in Book I of 'Essay Concerning the Human Understanding' (1690).
A more diluted version of empiricism holds not that all knowledge derives from experience but that experience does provide us with some knowledge not derivable in any other way. Except from experience how could I know how scarlet differs from purple ?
Innatism has been supported (in different ways) by Socrates, Leibniz and Chomsky.
'Empiricism' comes from the ancient Greek, 'empeira', which became 'experientia' in Latin and which we have adopted as 'experience'. What 'experience' is, is hardly totally clear. It may mean awareness of public objects such as tables and chairs, or awareness only of our own sense impressions (e.g. what I seem to see when I seem to see a table or chair). I can only briefly and incompletely indicate the possibilities here.
One point should be added, and that concerns the possibility of pure experience. It's a plausible view that all experience is informed by beliefs and expectations. It never occurs in an uninterpreted way. In other words (as some would say) we can have no pre-conceptual experience. That raises the question of whether at least some concepts are possessed prior to experience. If so, empiricism cannot rely purely on experience - or at least experience itself has conceptual preconditions and is not absolutely and solely basic to knowledge.
The literature is vast. Twentieth-century empiricism was represented by AJ Ayer, 'Language, Truth & Logic' (1936), CI Lewis, 'Analysis of Knowledge and Valuation' (1946) and B. Russell, 'Human Knowledge' (1948). Innatism is strong in the work of Noam Chomsky, 'Aspects of the Theory of Syntax' (1965). See also S. Stich, 'Innate Ideas' (1975). The online 'Stanford Encyclopedia of Philosophy' is useful for both exposition and criticism of empiricism and innatism.