One-liner
Reinvestment risk is basically the chance that, when a bond matures, you cannot put the money back to work at rates anywhere near today's.
Why it matters
You buy a bond paying a great , but as rates fall over the next few years, the cash coming back to you gets reinvested on worse terms. The income quietly fades with no one ever defaulting.
Analogy
You sign a short one-year lease, planning to renegotiate higher later. When the day comes the market is in a slump and the only tenants around will pay less than the last one. three years and you never face it.
The catch
A good rate only lasts until that bond matures. It does not buy you a return for life.