In law, a conviction is the verdict that results when a court of law finds a defendant guilty of a crime.
The opposite of a conviction is an acquittal (i.e. "not guilty"). (In Scotland there is also a third verdict of "not proven", which counts as an acquittal.)
For a host of reasons, the criminal justice system is not perfect and sometimes guilty defendants are acquitted while innocent people are convicted. Appeal mechanisms mitigate this problem to some extent. An error that results in the conviction of an innocent person is a miscarriage of justice.
After a defendant is convicted, the court determines the appropriate sentence as a punishment. Further, the conviction may lead to results beyond the terms of the sentence itself, such as loss of federal education loans in the case of a drug felony. Such ramifications are known as the collateral consequences of criminal charges.