Finnish language differs from many, many other languages spoken Europe in that it's Uralic, whereas most others are Indo-European. When it comes to language relations I (as a layman) would call Hungarian and Finnish sort of cousins whereas Estonian and Finnish are brothers and neighbours. That is to say, a Finn can guess the meanings of some basic forms of some very basic Hungarian words, but understand much of Estonian. Estonian and Finnish are very close relatives, as they are both Finnic languages. Finnic languages also include many spoken in certain nearby areas of Russia, although some of these languages are becoming extinct and most are weak in numbers. Therefore, the most common encounters between Finnic (and Uralic for that matter) languages happen between Finnish and Estonian.

To a person speaking Finnish as a mother tongue, Estonian often sounds funny, because many Estonian words are almost the same or not-very-commoly-used synonymes of the equivalent Finnish words. Estonian sort of sounds like someone speaking a strange and funny dialect of Finnish, although there certainly are many words whose meaning a Finn cannot guess. Many Finnish TV-comedians have played a character that speaks a sort of mock-overdone-Estonian, that's how funny it is for us. Usually this humour is based on the fact that the words are almost right, but not quite.

A real life example that might cause misuderstandings between an Estonian and a Finn is the Finnish word "piimä" which means soured milk. You see, in Estonian, "piim" means milk. Almost right, but not at all, as you can see.

An accurate and free online source of information (good enough for a layman) would be Wikipedia, The Free Encyclopedia, that has it's own section in English dedicated to the Finnish language. Enjoy.

Be sure to check out the interesting links that can be found at the bottom at that page, for example this one that shows the 2,253 (two-thousand-two-hundred-and-fifty-three) forms the Finnish language has for the word "kauppa" (shop).