If you lean on something, you incline your body against it, like the way you lean against a wall while waiting in line. If you lean on a person, you rely on her for moral support, like the way you lean on your best friend when you're feeling sad or worried.
If you’re tired, lean back in your chair. If you’re broke, lean on your family for financial help. But something can lean all by itself, if it’s not standing straight. The famous Tower of Pisa leans at an angle of about 4 degrees. As an adjective, we use lean to describe something skimpy or lacking excess flesh. When you're experiencing financial difficulty, you could say you're going through lean (not prosperous) times.