Quote:
Originally Posted by Baseball Prospectus
Leverage measures how important the situations a reliever has been used in are. A leverage of 1.00 is the same importance as the start of a game. Leverage values below one represent situations that are less important than the start of a game (such as mopup innings in a blowout). Leverage values above one represent situations with more importance (such as a closer protecting a one-run lead with bases loaded in the 9th inning).
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Baseball Prospectus | Glossary
You can also find a longer, more technical, explanation
at Fangraphs