If you have an ace high at the end of a Poker round, you haven't managed to get a pair, Three of a kind, or even a higher combination to begin with. Instead, the Player in question merely holds an ace in his hand, so the highest card is an ace. Accordingly, this is a "high card hand". More precisely, it is the strongest high card hand, since the ace is the most valuable card.
The chances of winning the Pot with an ace high depend on the poker variant played. While it is quite possible to win the pot with an ace high in Texas Hold'em, it is very unlikely in Omaha, for example, as it is much easier to form pairs here.
Alternatively, the term ace high is also used when a player has a straight or a flush with an ace as the highest card. In these examples, one would speak of an ace high straight or an ace high flush. These are also the strongest straight or flush hands.