An anvil's purpose in life is to be heavy and metallic.
An anvil is heavy so that cartoon characters have a rough life, and so that blows dealt to it will not have much chance of moving it. An anvil is metallic because the surface needs to be both flat and springy, and most metal is heavy enough by itself. Most anvils are made of low-carbon iron (steel) so that the blacksmith can shape the surface at his whim.
I bought a 50-pound anvil for $25(US) several years ago. It was not a very good anvil because it had been painted completely (to avoid rust? I couldn't tell) with a terrible gray that left pockmarks in the surface of the bick (and even some of the face) where it chipped off. These pockmarks showed up in the few pieces of metal (nails, construction scrap) that I hammered on. At least this wasn't something I did for a living. I found out later that a 'good' anvil weighing 50 pounds would have cost me about $300(US) at that time, so I guess I got an okay deal.
A 'typical' anvil has four parts: bick (also "horn"), face, tool-slot and feet. The anvil I bought had these. The bick is for 'round' or 'curved' shaping, and it is shaped like the cone portion of an ice-cream cone. The bick is like an extremity extending sideways from the body of the anvil. The face is the surface facing 'upwards' (away from the feet) on the body. The face starts soft but is quickly hammered solid. A good blacksmith will have a flat anvil face, without pockmarks or other unseemly markings; I was definitely not a good blacksmith. The tool-slot appears on an extension of the face opposite the bick. The tool-slot is square, sometimes accompanied by a small round slot nearby. The blacksmith will often make tools to fit in these slots; anything from "cutting" edges to specifically-honed "rounding" bits. The feet may be extended from the body somewhat, and are often designed with bolt-slots for mounting purposes.
You're probably wanting to see what an anvil looks like, so here's my attempt:
SIDE VIEW
tool slot
V
..................
... ..........
... body . bick .
.. . .
.. . .
.. ........ .
..... ..... <--feet
..... .....
TOP VIEW
..................
. .....
. ... face . ......
. ... . ......
. .....
..................
Well, the top view isn't worth much, but that's what my anvil looked like.