To rebound is to come back from a slump. You might rebound from an illness, or your country might rebound from an economic recession.
Like many words that start with the prefix re, rebound involves something happening again. In this case, to rebound is to bounce back to a previous state or condition. If you gain 20 pounds and then lose it, you rebound. If the stock market crashes and then returns to a healthy level, it rebounds.