I'd like to think of "L3 switch" as being short for switch with layer 3 functions.
Often they are used for routing traffic between VLANs. A router can do that as well but a L3 switch can usually do faster and on more ports at the same time.
Typical is to have a bunch of L2 switches where the end points connect and then the L2 switches are uplinked to one L3 switch that takes care connecting the L2 switches together and do inter-VLAN routing.
There are also L3 Lite switches (aka L2+) which are L2 switches with a limited L3 functionality like for instance static routing.
L3 switches are usually the ones with the most features in all categories so sometimes you need to buy a L3 switch because you are after some other feature, like redundant power or what not.
In small networks L3 switches are usually not needed.
As an example Dell's PowerSwitches for instance are managed switches for building out the network to end points (campus).
They are like this:
N1100 series - L2 switch N1500 series - L3 Lite switch N2000, N3000 series - L3 switchThey have the same OS and work the same but each step up in the series gives you more features and more speed and higher cost.
