This is a sixteenth note.
It lasts for one quarter of a beat.
There are four sixteenth notes in one beat.
There are 16 sixteenth notes in one bar of four four time.
Here is a Bluegrass flatpicking part which uses sixteenth notes. Take it slowly until you can play all the notes clearly and evenly and then speed it up.
Here is a variation on the previous example containing lots of slurs.