What actually happens with hyperextension in your knee?

Too much motion. The knee is overly extending and moving past the point that it should due to its weak or damaged soft tissue support structures.
Injury to ligaments. Hyperextension implies that the knee is moving beyond its normal range of motion. The ligaments and tendons typically prevent this from happening in normal activities. A blow to the knee can push the ligaments and/or tendons beyond their normal resilience. This can lead to strain, sprain or tear and varying degrees of each.