Definition of range
A poker player's range is his range of possible hands. By fan, we mean "all possible hands depending on the player, his position and the previous action". For example, preflop, all players have a range of 100%, meaning that they have been dealt 2 random cards and can have any of the 1326 possible combinations. Now, let's say a player raises preflop; here, his range is no longer 100%. If he is in the early position, his range is even smaller. So, he goes from a range of 100% to, say, a range of range%. A range is a range of possible hands at any given time.
What is the point of knowing a player's range?
To make good calls and good folds! When you play a hand, you think about your cards, how they connect with the community cards, but also about your opponent's range to see how your hand is doing against their range. For example, a player calls in the UTG position. You call in SB position with 88. The flop falls 2-5-7. Your opponent bets and you call. The turn is a J. Your opponent bets or you call. The river is an A and he pushes all in. Every time he bets, his range shrinks. Here, your opponent might have a range of AA, AK, AJ, JJ, 77, AQ. His range of bluff is very limited. Against such a range, your 88 is a fold on the river. Against such a huge range, it could be a call.