Usually, users get suspended on Instagram for doing one of the following things:
- Trolling other users
- Posting inappropriate images
- Abusing the service by trying to "game the system". This usually relates to buying followers, taking part in followback chains, or other behavior which Instagram has ruled out in its terms of use.
Most of the time, suspensions on Instagram are temporary, although the network does reserve the right to block you from using the site permanently.