Accounts are generally suspended for violations of the Twitter Rules. We also may suspend accounts for investigation if we suspect an account has been hacked or compromised.
If your account is suspended, you should see the nag below when you are logged in:
To expedite the appeal process, please check to make sure your account is currently suspended by logging in.
If your account was suspended for aggressive following behaviors, you'll need to confirm that you've removed all prohibited following automation from your account, and will stop any manual aggressive following behavior. You can find information on following automations and permitted following behaviors on the Following Best Practices help page.
File a help request here.