Literally it means a shadow, or more specifically the a partial shadow at the edge of a shadow, from paene (almost, nearly) and umbra (shadow).
In legal theories about rights and powers, penumbra means a right or set of rights that is implied by a formally stated right, or powers that are implied by a law.
The legal definitions are not firm or well-defined, as they come from figurative uses by a relatively small number of findings in terms of US federal law. The best known is Justice Arthur Goldberg's Opinion of the Court in Griswold v. Connecticut 1965. Here he used the term several times, most famously in:
The foregoing cases suggest that specific guarantees in the Bill of Rights have penumbras, formed by emanations from those guarantees that help give them life and substance.
This not only had the specific case of demonstrating a right to privacy as entailed in the Bill of Rights, and by extension rule Connecticut ban on contraceptives unconstitutional, but had a strong influence on later legal thinking that affected some particularly controversial cases (Roe v. Wade 1973, perhaps the most so).
The figurative use though goes back earlier, to Montgomery v. Bevans 1871.
Being a figurative use, the exact meaning has differed in different cases, but "right that is implied by another right" is a good rough definition.