A placement test is a special kind of test on Duolingo at the beginning that allows users (with previous experience in the language) to test their skills in the target language.
The test takes several minutes and is an approximate estimation of a user's skills. So users may test out of one skill, one-fourth of the tree, or even the whole tree itself (it depends on how many questions the user answers correctly). The test also awards points equivalent to completing each individual skill. Apparently placement test can give any multiple of 10 XP from 0 to 100.