Grades are a label attached to scores in osu! that reflect the "quality" of a play.
List[]
These are listed in order of quality, from best to worst.
SS[]
In some records, SS is referred to as X.
This is the best obtainable grade in osu!. Scores must have 100% accuracy on a map in order to achieve an SS/X.
S[]

Getting an S Rank.
A common grade, requiring 0 misses, over 90% 300s hit and less than 1% 50s hit. Thus, an S signifies either an FC or that the player only combobroke from sliderbreaks.
A[]
Another common grade, usually gotten through scores with a few misses or low-accuracy 0-misses/FCs. Specifically, if you've missed an A requires at least 90% 300s hit, otherwise the standard decreases to 80% 300s hit.
B[]
A common grade when passing a beatmap. This is the lowest grade whose standards change with 0 misses. A B is achieved with at least 80% 300s hit, lowered to >70% 300s with 0 misses.
C[]
Another common grade when passing a beatmap, gotten with at least 60% 300s hit.
D[]
The worst grade submittable, signifying the lowest accuracy. If the player fails to meet the standard for a C grade or higher then they end up with a D grade.
Silver variant[]
The silver variants of the S and SS/X grades are obtained if the player has used at least 1 visibility mod (Hidden, Flashlight and in osu!mania, Fade-In).
In plain text, 'H' is appended to the grade (SH and SSH/XH respectively).