Its the first major round of financing from a Venture Capitalist. Typically, it is after seed money, but you could go straight to a Series A without prior investments. Subsequent VC rounds count down the alphabet: Series B, Series C, etc..
Roughly, yes, but sometimes VCs do smaller seed deals that don't count as series As.
Though there's no precise definition, a series A round steps up things up a level in seriousness. It's usually quite a large amount of money (at least $500k, usually millions); the paperwork is a huge binder instead of a few sheets of paper stapled together; the terms are fairly draconian; and the investors get at least one and possibly two board seats.
