The basic idea of account suspensions is laid out in Jeff Atwood's announcing blog post A Day in the Penalty Box. They are timed periods during which the account cannot interact with the site in any way, save passively reading. These are given by site moderators (which includes SE employees) to users who have exhibited a tendency towards disruptive and/or unwanted behaviour.
Each suspension comes with a message/email from the suspending moderator explaining the reason and duration of the suspension. This message can be replied to (but only once, unless a moderator responds to that). We've seen replies that run the gamut from the succinct but unhelpful
to reasoned and rational responses that convince us that one of the main purposes of the suspension — to effect a change in the user's behaviour — has already been reached. (And, yes, suspensions can end before their stated end-date at the discretion of the moderators.)
Usually the moderators do not discus the specifics of suspensions on meta or on chat, especially while the suspension is on-going.
As of now, when a user is suspended their profile will show one of the following reasons (from Marc Gravell's answer on Meta Stack Exchange):
- for voting irregularities When the user's voting habits are contrary to their intent: to signal that content is good or bad. This covers a lot of situations such as upvoting your own content via sock puppets, serial downvoting of the content of specific users, and even the serial upvoting of the content of specific users. (Votes are meant to judge the quality of a post, not the quality of the person making the post.)
- for promotional content When a user's contribution, though perhaps actually answering questions, tend to also (or primarily) promote their own products or services without disclosing the connection. If you want to say that your commercial Maple plug-in solves such-and-such a problem, you should be clear that you're not a random person recommending a product, but that you are involved in its development.
- because of low-quality contributions This is pretty self-explanatory, but if over a period of time a user is not contributing positive content to the site, that account could be suspended. This isn't overly common, as there are automatic rolling rate limits and outright blocks.
- to cool down Basically everything else, from consistently ignoring the Be Nice policy or abusing other privileges, to an account is acting strangely and out of character and we want to put a temporary halt to the actions and reach out in case the account has been hacked. This is generally used when a user has been disruptive to the community in a sense not covered by the above.