Solemnities are the highest rank of feast (and if you look at the official English title for the day it usually includes the word “solemnity”). Solemnities are NEVER days of abstinence from meat but feasts can be.
In general, solemnities include the days that are listed as Holy Days of Obligation on the worldwide Church calendar (some of which are not days of obligation in all countries or are always transferred to Sundays) as well as all days in the Octave of Easter and some other days that always fall on Sundays.
In addition there are local solemnities such as feast days of national patron saints and feast days/dedication days for local parishes.