Earnings per share (EPS) is a company's net profit for a period divided by its number of outstanding shares. A company that earned $1 billion with 500 million shares outstanding has an EPS of $2 — each share's notional claim on that year's profit.
EPS is the denominator in the P/E ratio and one of the most closely watched numbers in a quarterly earnings report: a company beating or missing analysts' EPS estimates by even a few cents routinely moves the stock price the same day, because it's read as a signal about whether the business is executing as expected.
"TTM" (trailing twelve months) EPS is calculated from the last four actual reported quarters. It differs from "forward" EPS, which is an analyst estimate of the next twelve months and is inherently a prediction rather than a reported fact.