EPS converts total profit into a per-share figure, which is what lets you compare a company against its own past and against its price. Diluted EPS is the conservative version, assuming every option and convertible in issue becomes a share.
It can grow without the business growing. A large buyback shrinks the share count, so the same net profit produces a higher EPS. Checking whether profit or share count did the work is a two-minute test that changes the interpretation entirely.
Watch the gap between reported and adjusted EPS. Adjusted figures exclude items management considers non-recurring, and a company where those exclusions recur every single quarter is telling you something about the quality of its earnings.