Redial is the phone function that calls the number you dialed last with a single button. If the line was busy (a busy tone) or nobody picked up, you can try again without keying in the number a second time. On a landline it is the "Redial" button; on a smartphone you tap the most recent entry in the call log.
Redial goes back a long way. It was already built into sets from the era of the push-button phone. The dial-operated black phone had no redial at all, so every call meant turning the dial again. Only with electronic handsets did it become possible to hold the last number in memory and send it again at the touch of a button.
Auto-redial repeats the call automatically at set intervals while the line stays busy. People use it for ticket sales and reservations at popular restaurants, where the lines are congested, but from the other end it looks like a burst of repeated incoming calls. Hammering a line every few seconds can come across as harassment, so space the attempts out and cap how many you make.
Smartphones have no separate redial button. You reach back through the outgoing and incoming call lists and tap a number to call it again. That makes any past contact reachable, not just the last one, but it also makes calling back an unfamiliar number far too easy. Some schemes leave you paying a steep call charge or information fee at the other end, so with a number you do not recognize it is safer to look up who it belongs to from your call history before deciding. One-ring calls explained walks through the usual pattern. A call back can also be the opening move in a special fraud attempt to draw out personal information.