How can one hide their reputation? I am pretty sure I came across different profiles with hidden reputation, where their actual reputation was replaced with the number 1.
In addition to goldPseudo's answer which discusses suspension, we can...
Stop reputation showing on our devices: It's possible to locally hide reputation from view by using a script, e.g., Hide all pointless user data (gravatar, badges, and reputation). The reputation will still exist and everyone else will still see it, but on the device the script is installed on it won't display. The motivation behind this is to avoid voting based on the answerer's reputation.
Give away reputation: I've occasionally seen users who prefer not to have high reputation (e.g., in order to avoid seeing all the deleted posts), in which case, reputation can be given away in the form of bounties.
Create a new account: I recall a user at math.SE who created a new account each time they reached a high enough reputation; it was quite confusing at times.
The primary reason for these instances of "1" rep on established accounts is laid out in goldPseudo's answer. Not mentioned there however is that such suspensions are always temporary and in the hopes that the user will fix whatever problem led to the suspension when participating in the future. Each user's suspended account will show a banner at the top that shows a category reason (without specifics) for why the user was suspended as well as the date when the suspension will be lifted.
The exact reasons for suspensions is only visible to moderators (and SE staff who audit them) and are not given out publicly to other users. Also the posts or comments which let to needing a suspension are usually cleaned up as well, so don't make the mistake of thinking that just because you see good posts from a user that their suspension was unjustified. The problematic posts have been removed and what you see left is the good ones.