The Zohar (and the Sulam even more so) refers to 'Zer Anpin', usually in relationship to other middos/bechinos such as Malchus. What does Zer Anpin mean?
Ze'eir Anpin is the name of one of the partzufim, which is a term someone asked about recently: What is a parzuf?
In general, if you're familiar with the idea of the sefirot, Ze'eir Anpin correlates to the six sefirot Hesed, Gevurah, Tif'eret, Netzah, Hod, Yesod. These sefirot are often considered aspects of the single sefirah Tif'eret. So, you could think of Ze'eir Anpin as a name for the sefirah Tif'eret.
The sense of the name seems to have to do with a contrast to Arikh Anpin, which is the name of the partzuf that correlates to the sefirah of Keter, and which means 'long-tolerant', 'forgiving', 'merciful' (erekh appayyim in Hebrew): if that level is a level of pure loving-kindness without end, then Ze'eir Anpin, which would literally mean something like 'short-of-tolerance' [relative to Arikh Anpin], would be a blending or balancing of kindness and severity.