I’m not a real expert at these kinds of things, but as I understand it the terms imply differences in evolutionary history. Two genes are paralogous if their common ancestor is within the same species. Usually (exclusively?) this is a gene duplication event. The two genes then continue to diverge from each other within the species. If the common ancestor of two genes comes before two species diverged, then the two genes are orthologous. As to why it is important—I guess it matters most to people who have to construct and interpret evolutionary trees of one sort or another. Not my department, I’m afraid.
blcr11 is on the right track. If you’re doing phylogeny work, it is absolutely important that you are dealing with orthologues rather than paralogues. Orthologues are the same genes in different species, paralogues are different genes within one species, but members of the same gene family. Apples and oranges are orthologues. MacIntoshes and Spartans are paralogues. (I’m being free with my analogies here.)