Star rating (SR) describes a beatmap's difficulty, which is automatically calculated by the osu! client. Star rating plays a large role in how performance points are awarded. This number can be seen on the song selection screen and on a beatmap's info page.
Main page: Difficulty
On the website, beatmaps are automatically given a difficulty icon based on these star rating ranges:
Most maps' intended difficulty levels match the icons they are given, but some deviate significantly. This is why the ranking criteria defines more precise rules for determining difficulty and evaluating beatmapset spreads.