Multiple Payline Slots, otherwise known as Multi Line Slots, are slots game with more than one payline; and therefore offer the player a greater chance of winning. When playing a Multi Line Slot you are effectively playing a number simultaneous games at once, for example, if you are playing a slots game with the option of 15 paylines, then you can active all 15 paylines and therefore, in theory at least, possibly win x15 times; once for every payline. If a player wishes, they can lower the number of paylines, normally down to one, depending upon how large or small the amount of their wager.
Multi Payline Slots game have a Paytable displaying all of the possible winning combinations. These paytables vary slightly from casino to casino but there are generally two types, as shown below. The first depicts the combinations using lines and the other using coloured blocks and both tables are showing you the same thing. Clicking on the 'Paytable' link before you start playing a slot game will give you all of the possible winning combinations in that game.

15 Payline Paytable in Lines. |

15 Payline Paytable in Blocks. |
Multi Payline Slots can have all of the usual slots features such as progressive jackpots, varying numbers of reels and scatter, wild and gamble features.