The batter's success rate of "1 for 1" means he got a hit and was on base in his only attempt at batting so far in the game.
Similarly, if he was out (or struck out) in his next two trips to the plate, he would only be "1 for 3."
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It means that a player had 5 official At Bats in the game (or some other timeframe) and got 4 Hits. That wouldn't include walks, sacrifices, or other types of plate appearances that don't count as an official At Bat.