Stale share: The share was submitted too late (probably because of the high latency or problems with connection). This is the only share that is expected to happen in small quantities thus it is considered normal.
Share above target: There is a problem with your mining software that needs to be inspected or configured properly. It is also possible that the mining software is not compatible with NiceHash.
Duplicated share: The share was submitted more than once and indicates a bug in your mining software or incompatibility with NiceHash.
Other: Any other type of rejected shares usually means a bug in your mining software.
You can find the type of rejected share by checking your mining stats, when you inspect the detailed mining stats for individual algorithm.