An eagle in golf is a score of two strokes under par on a single hole, such as a 3 on a par-5 or a 2 on a par-4.
Golf names its under-par scores after birds, and each bigger bird means a better score. A birdie is one under par, so the eagle, a relatively large bird, was chosen for the step beyond it. An eagle usually happens when a golfer hits the ball far enough to reach the green in fewer strokes than expected. That is why eagles are most common on par-5 holes, though they also happen on short par-4s. A hole-in-one on a par-3 also counts as an eagle. One stroke better, three under par, is an albatross, which Americans also call a double eagle. Four under par is an unofficial score called a condor, which has never been made in a professional tournament.
Source: Wikipedia, Par (score)
Image: Golf putting on green, Woodypino, CC0, via Wikimedia Commons.