What do the tattoos on Sirius Black's chest mean?

It is the alchemical symbol for Amalgamation.

Below it he has the rune Ansuz

The answer on Sirius' chest is basically imprints that have been printed once he has entered prison. (When he went to Azkaban, he got "prisoner tattoos"). Usually, criminals are given tattoos as numbers in jail ex. Criminal #2323. Sirius' tattoo was basically just that, a tattoo received from his time in Azkaban Prison.

The large tattoo on Sirius Black's chest is very similar to the symbol for the planet Neptune. The only difference is the tattoo on Sirius Black is missing the center prong in the trident like symbol. In roman mythology Neptune was god of the sea, which is interesting since Neptune's interior is mostly made up of ice and rock.