Good for you!This thing is Very useful!
It isn't an "anvil"(pedantry!I know you love it

,although it is called a "stake-anvil"(or more commonly a "beak"or "bick").
As it's name implies it is an anvil-shaped stake,a bottom-tool.
It used to be a very important tool in any shop.The "beak",or rounded side is for welding and shaping sockets of all sorts,without it any socket work is a pain.
(i've had to build one as i needed it,and it was a lot of work and hassle,and of course will never be as handy as a factory tool).
The square-section counter is for shaping and truing-up of assorted square-ish recesses,like hinge-joints(where i at times sorely missed something very like it).
If of good quality,the top face of it will be at slightly under 90 degrees to the sides,so that you Can shape an accurate 90...
This tool has a very good base.Of course it's not meant to go into a "stump",it is sized and shaped to fit into a special recess in a swage block,or an iron-man...Sometimes in a hardy hole of an anvil,tho' it'd then have to be a dedicated anvil and set up lower than usual.
But the germane thing about it's general arrangement is that it's "body"'s Mass is arranged directly under where you'd be likely to strike it-the small flat face-and is about equal in section.That will make the energy transmit all the way through the tool,giving you the most return on your energy invested.
All that is just some very general pedantry...Forging is a very precise science,there's a Lot of thought and precision of method...
I know that i do go on and On in an nagging,and no doubt annoying manner...I do apologise for that...It's just that to Me it contains Lots of info that is very pertinent...