Minos was a judge in the underworld in Greek mythology and has a similar role in Dante's poem. Upon entering hell, souls go to see Minos in the second circle of hell and confess their sins. Minos wraps his monstrous tail around him a certain number of times, and this corresponds to the numbered circle of hell that the soul must go to.
The timeline below shows where the character Minos appears in Inferno. The colored dots and icons indicate which themes are associated with that appearance.
...second circle of hell, where there is more suffering and screaming. Dante sees the monstrous Minos, the judge of the underworld in Greek mythology, judging and sentencing souls. When souls come... (full context)