An XLR is a circular, usually three-pronged, cable used commonly for carrying audio signals.
The origin of the name is a long story. The "X" comes from the "Cannon X" series, its original manufacturer. The "L" comes from a latching mechanism that was added later on. The "R" comes from the rubber insulation found around the cable.
A quarter-inch cable (also sometimes called a "microphone cable" or a "patch cable") is frequently used along with XLRs to carry audio signals. You'll use this cable for most instruments that need additional amplification or sound processing before the signal is sent to a speaker.
It's so named because the ends fo the cable are 1/4 of an inch in diameter.
A 3.5 mm cable is the cable used by most headphones and earbuds today. It's so named because the ends of the cable are 3.5 mm in diameter.