The California Commission on Peace Officer Standards and Training (POST) wrote the PELLETB and keeps it. Its full name is the POST Entry-Level Law Enforcement Test Battery, and California departments also call it the PELLET-B, the POST test or the POST reading and writing test. Regulation 1951 requires every California peace officer candidate to show reading and writing ability, and this battery is POST's own test for it. The regulation also allows another validated test, so some departments use a different one (California).
The test is aptitude, not knowledge. You won't be asked about laws, procedures or police work, and nothing on it needs a calculator. What it does test, in two parts: writing (clarity, vocabulary, spelling) and reading comprehension.
Outside California, “POST test” often means a different exam, the NPOST, from another publisher. If a posting in another state asks for a POST test, check which one it means before you study.