if i have for example a scores table:
user game score timestamp 1 50 50 date 2 60 40 date 3 70 25 date 4 80 18
As you're not using a GROUP clause, the max function is returning the maximum value from across the table. As such, if you want to return the matching data for the highest score, you'd need to:
SELECT * FROM table_name ORDER BY score DESC LIMIT 1