Non-Chasidic Ashkenazim wrap their tefilin shel yad inward toward the body when coming over the top of the arm, while Sefardim and Chasidim wrap outward away from the body when coming over the top of the arm. What is the origin of this dispute, the earliest extant sources for each custom, and the meanings and significance ascribed to them?
The actual dispute is not about which direction to wrap, but the location of the loop through which the retzua is threaded. We find this dispute in the Biur Halacha (27:2 ד"ה המנהג), he quotes the Beis Yosef in the name of the Mahari Ben-Chaviv who holds that while the "yud" should be located at the bottom of the tefillah the loop should be located at the top. The Biur Halacha then quotes the Darkei Moshe who claims that it is preferable to have this loop directly next to the "yud" on the bottom of the tefillah. This is also the opinion of the Bahag who says that the loop should be closer to the heart (just like the "yud") and the Rosh.
The Biur Halacha adds that he feels that the location of the knot is not me'akev and therefore one should follow his custom.
To add a bit of "Chassidish" meaning, I was once told by a Lubavitch Chassid that one should wrap out, as opposed to in, to remind himself that he should give before he takes.