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 * 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.
When sixteenth notes are played in conjunction with eighth notes the following timing combinations occur. An easy way to remember these combinations is that they have the same timing as saying the words chucka-boom and boom-chucka.
Here is Arkansas Traveler again. This time it is in the key of G and is written in eighth and sixteenth notes.