Inside and outside bets refer to the options on the betting layout. Inside bets are all the individual numbers from 0 to 36, plus small groups of numbers that share a line or an intersection on the layout.
Outside bets refer to the options on the edge of the layout, and are larger groups of numbers that tend to have simple or even odds. For example, Black or White, Odd or Even, High or Low, to groups of 12 numbers.
You have a higher probability of winning with outside bets, and therefore payout is lower. Inside bets have a lower probability and therefore have a higher payout. An inside bet that is a straight bet one one specific number has the lowest probability and therefore pays out the most.