well for guitar im not sure but for string instruments t means you play the note as either half or 16th notes..
for example on the picture you see a quarer note that has the two lines. n this case you would play 2 8th notes instead of the one quarter note at that spot....it basically just makes it easier to read and saves room
Actually, it says "mandolin arranged for guitar" - it's tremolo alright, but seeing how a mandolin is usually played, it'd be quite tedious to write all the notes as single ones.