The "A" in the name comes from the use of Series A Preferred Stock, the securities issued in the round. A funding or financing round in which Series A preferred stock is issued and sold. Series A Preferred Stock is typically sold to outside investors.
Usually Series A preferred Stock is sold to the first institutional investor(s) in a company. Sometimes this is a first venture capital financing round, but more usually this round would be comprised of angel investors or other sophisticated individual investors. This round can be effectuated through a private offering or a public offering, but most are private offerings relying on an exemption from registration requirements under the U.S. Securities Act. Subsequent preferred stock funding rounds are usually referred to as "B," "C," "D," and so on, although in some cases it can be preferable to number subsequent preferred stock funding rounds "A-1," "A-2," and so on.