A trill is an ornament that is often used to accentuate a note or simply to add some variety on a repetition. Trills are very common in the baroque period (music of Bach, Scarlatti and Weiss for example) but they are found in all periods of music. Used tastefully, trills can give sophistication and personality to a piece and they also offer room for creativity on the players behalf.
Trills and ornamentation can get quite complex, but in this lesson we are just going to look at a very basic trill that you might use in a simple baroque piece. The left hand trill is more often than not a series of slurs (If you need to learn about slurs have a look at my lesson on slurs here). Instead of just playing two notes, the plucked followed by a slur, you can keep creating slurs between the two notes for a longer duration.