In poker, there are different sizes of bets which are used to throw in wager amounts. From the smallest to the biggest wagered amount, all bets are valid as long as they meet the minimum required amount. Therefore, a big bet here is referred to as the biggest size of a bet wagered by a poker player. For example, in some games with fixed limits, the amount of the biggest bet keeps increasing especially in later rounds.
This is where the difference is seen between the biggest and smallest amounts that were thrown into the pot as bets. So for a 5 - 10 Texas Hold 'em play, the big bets sizes are for $10 while the small sizes go for $5. The same thing applies to other types of poker games where you have the small and big bets chosen at random by the players who wish to wager a particular amount of their choice.