What does son las tres y veinte mean?

This phrase means "It is 3:20" referring to the time on the clock.

'Son' is a conjugation of the verb 'ser' and refers to any hour of the day besides 1:00.

'Las' is used to refer to 'las horas' or 'the hours'.

'Tres' means 3, so you know we are talking about 3:00.

'Y' is used to show that we are about to discuss the minutes of the 3:00 hour.

'Viente' means 20, so you know the time is 3:20.

In Spanish, it is often common to not say the specific time, if there are alternatives. For instance, for "It is 3:15" it is often said "Son las tres y cuarto" - 'cuarto' meaning quarter, for quarter of the hour, which is 15 minutes. For "It is 3:30," it would be more common to hear "Son las tres y media" - 'media' meaning half, so half of the hour.