Each poker hand is ranked in a set order. The higher the rank, the less chance statistically you have of getting it. The higher the rank of your hand the better, because two pairs always beats one pair, and a flush always beats a straight.

What happens when there are two two pairs?

If two players both have two pair, the winner is determined by comparing (1) the higher pair, (2) the lower pair, and (3) the fifth card in the hand. Player 1 has AA229, which beats JJ99A, because aces beat jacks and there's no need to go further.

Does a pair beat a pair?

a two pair beats a one pair; a three-of-a-kind beats a two pair; a straight beats a three-of-a-kind; ... a Royal Flush beats a straight flush.