Ornaments are added to sheet music to add a flourish to the notes played.
These two kinds of grace notes add a note before the main one:
acciaccatura / crushed note - play the extra note briefly, with emphasis on the main note
appoggiatura - play the extra note, then the main note (equal value)
These add notes afterwards:
mordent - play the note, one above, then the note again
lower mordent (inverted) - play the note, one below, then the note again
trill - quickly alternate between the note and one above
turn - play note above, note, note below, note
turn after - play note, then note above, note, note below, note
inverted turn - play note below, note, note above, note
Read more: [Wikipedia]