EPS is reported quarterly. What moves the stock is not the number itself but the gap between it and the consensus estimate, along with guidance for the next period. Companies also report adjusted EPS, which excludes items they consider one-off.
EPS feeds the pe-ratio and is the denominator in most valuation shortcuts.
Example: net income of $500 million and 200 million shares gives EPS of $2.50. If analysts expected $2.30, that is a beat of about 9%.
Related: pe-ratio, earnings-report, guidance, earnings-call