The authorship of the gospels is tricky, as they were all initially anonymous before later tradition ascribed authors to them. The Gospel of Mark is, originally, anonymous. We attach Mark to this particular gospel because the bishop Papias of Hierapolis did so around the year 100, himself referring an earlier tradition:
Mark, in his capacity as Peter’s interpreter, wrote down accurately as many things as he recalled from memory—though not in an ordered form—of the things either said or done by the Lord.
If this is to be believed, as the Church traditionally has, then the Gospel of Mark was written by the disciple Mark as an account of St. Peter’s recollections. The Gospel of Mark holds an interesting place in Christian scripture as the oldest canonical gospel and one of the direct sources for two of the other canonical gospels, the Gospels of Luke and Matthew. According to biblical scholarship, the Gospel of Mark was used as a basis for material for both Luke’s and Matthew’s gospels.
As for why, the Gospel of Mark seems to be written to reach Greek Christians who were mostly unfamiliar with Judaism and the Jewish context for a Messiah. The author of this gospel certainly wrote for a Greek-speaking Christian audience, as the language itself was Greek and the author explains Jewish customs and Aramaic terms to his readers. Interestingly, many scholars discredit Papias and his claim that the contents of the gospel were based on Peter's recollection; making that link would in turn make the Gospel of Mark a more authoritative and reliable document.