In Russian you say "я говорю по-русски" (ya govoryu po-russki) to say "I speak Russian". What does the "по" mean there?
First of all, like Matt pointed out, it's ja govorju.
Po is (or in this case, was) a preposition used here in its original meaning of "after/following" (its primary meaning in modern Russian is "over/across [a surface or medium]"). It's not technically a preposition anymore, as po-russki has long solidified as an adverb.
Curiously enough, though, it solidified in a form that would've been considered bad grammar in the Middle Ages. Po-russki blends together what were historically two different expressions: po rus’sku, "after the Russian [way/fashion]" — cf. modern Polish po polsku — and rus’sky, meaning "with [those things that are] Russian", cf. modern Czech česky. Slovak is another "offender" here with its similarly fused-together po slovensky.
In case you're wondering how "those things that are" got into something as simple-sounding as rus’sky/russki: this is the now-defunct instrumental case of the (also now-defunct) russka(ja), a nounless adjective that looks feminine singular but is actually neuter plural. It's the same nounless neuter plural that was extensively used in Ancient Greek and Latin. (It's how we got words like agenda, literally something like "the to-be-dones".)
First of all, "ja govorim" is wrong (though it may be ok in other Slavic languages, such as Serbian). In Russian it could only be "я говорю" (ja govorju).
Next, as "по-" is written together with the rest of the word (the dash doesn't matter here), it means that grammatically it's considered to be simply a prefix, which is used to form adverbs out of adjectives and possessive pronouns, e.g.: по-хорошему, по-моему, по-английски etc.
Thus "по-русски" is just the word "Russian" used as an adverb. You may also think it as something close to "in the Russian way", "as Russians do" or anything like that.
I believe this question is also related to: “На английском” or “по-английски”?