Rolling avoids settlement or delivery. Index futures roll around the second Thursday of the expiry month; other products have their own conventions. Continuous charts stitch months together and can show a roll gap that never actually traded.
The roll has a cost: the price difference between months plus two spreads. In contango a long position rolls to a higher price; in backwardation to a lower one.
Example: you are long ESU at 5,000 and ESZ trades at 5,030 because of carry. Rolling means selling ESU and buying ESZ; your position is now measured against 5,030.
Related: contract-month, front-month, contango, backwardation, first-notice-day