The difference is purely grammatical. Please compare the following sentences:
Ты знаешь меня. (You know me.)
Я знаю тебя. ( I know you.)
Both ты and тебя are translated as "you", but they have different grammatical functions. In the first sentence ты is the subject of the sentence. And subjects in Russian sentences are always in the Nominative case.
In the second sentence тебя is an object, because the subject in this sentence is я (I). Objects in Russian sentences are expressed by other cases, such as accusative, for example.
The English word "you" doesn't reflect these changes, however, other English pronouns do have different forms (e.g. I - me; he - him; she - her; they - them)