To posit something is to assume or suggest that it is true. You can posit an idea or opinion.
When you posit, you submit an idea or give an opinion. Scientists posit many ideas — called hypotheses — that they then try to prove or disprove through experimentation and research. In science, you hear about positing a lot, and the same is true in math and logic. When you say "If X, then Y" you're positing a proposition. Positing can also mean to put something somewhere firmly — this means to deposit, fix, or situate.