Minhag Ashkenaz is the Jewish tradition of Northern Europe. The first records of Jews in what is modern day Germany dates back to the 5th century. The tradition of these Jews is a combination of the customs of Jerusalem and Babylonia. The Ashkenazi tradition moved east over the centuries in Poland and other Eastern European counties where the customs evolved further. Minhag Ashkenaz specifically refers to this unaltered Northern European/German tradition.
What differentiates Minhag Ashkenaz from the rest of European Jewry is primarily Tefilo (prayer). There are several differences here, but the most notable is the use of Piyutim (poems) in certain sections. These Piyutim are said on special occasions such as holidays and days of special Torah readings. A great resource for Piyutim in Teflio is Machzor Shivchei Yeshurun by David J. Roth. Unfortunately my siddur does not contain any of these Piyutim, but indicates when some of them should be said.
Just a sample of the differences of Minhag outside of the Nusach HaTefilo are: young, unmarried, boys wear a Talis, washing & Al Netilas Yedayim before saying Kiddush, the use of a Winpel during a Bris. Most of these minhagim have their source in the Sefer Maharil. The most influential Modern progenitor of Minhag Ashkenaz is Rabbi Binyomin Hamburger. K’hal Adas Yeshurun in Jerusalem has an online forum with a lot of information. You can check it out here.