This is a great question. Here is a brief etymological explanation of the name, "Jesus."
Jesus is from Yeshua, which was a common alternate for Joshua (Yehoshuah). This later came to be transliterated to Iesous in Greek. From the Greek, it was translated into Latin, Iesus, which is essentially what we have in English. Latin has no "j" in its alphabet. So, we can say that we get the name, Jesus from Hebrew through either the Greek or Latin.
As for meaning, we need to go back to Yehoshuah or Joshua. When we do this, we can say that it means, "He saves." The verbal form Yehoshuah or Joshua means, "to save." We also get a theological sense of this meaning even in Mathew's gospel. Matthew 1:21 states: "She will bear a Son; and you shall call His name Jesus, for He will save His people from their sins."