When you bleed, blood runs or oozes out of your body. Cutting your finger when you're chopping vegetables can make you bleed.
Some kind of illness or injury, particularly one that cuts or scrapes your skin, can make you bleed. In long ago days of medical care, doctors would deliberately bleed patients to treat specific conditions, though today we mainly bleed due to accidents. You can also use bleed to mean "drain of money or resources," as when a greedy relative bleeds his wealthy grandmother, using her fortune to buy himself fancy cars.