Double Spending Problem
Double spending is the risk that the same digital coin is spent twice; blockchains exist largely to prevent it.
In depth
Digital files copy perfectly, so before Bitcoin any digital cash needed a central server to check each coin had not been used already. A blockchain solves this by having the whole network agree on transaction order — once a coin is spent in a confirmed block, a conflicting spend is rejected everywhere. Waiting for confirmations is how you avoid accepting a spend that could still be reversed.
Why it matters
It is the core problem Bitcoin solved and the reason confirmations exist.