Single Payline games will only pay out for winning combinations displayed along the central line of the reels. You can recognise them because they will usually have a table showing the different amounts that can be won when you bet more than one coin.
Multiple Payline games can pay out for winning combinations on up to 5 lines, going across the top, middle and bottom of the reels, and diagonally from corner to corner. You can select how many of these paylines you want to bet on each time you spin. Betting on multiple paylines usually costs one coin per payline.