Something that's admissible is allowed or relevant. Admissible evidence in court is evidence that a judge permits to be brought forward.
Evidence that's admissible is valid — it has some measure of reliability, and it makes sense in the context of a particular trial. You'll almost always find the adjective admissible describing such evidence, though the word had been around for about 200 years before it gained this legal meaning. Its Latin root is admittere, "to allow to enter, let in, or give access."