ID is the only one UNIQUE field in database. ID is generated AUTOMATICALLY. There can not be 2 the same IDs in one database.
You can view user's ID by mouse-overing on his "Member" title, for example. There will be kind of string:
The part after "user" is user's ID. For example, your user ID is 255.
Searching by ID is kind of rare thing. It is useful for example if you know user ID and want to see email of him, if it is hidden. Basically, the most popular searches could be by Email and Nickname.
As Admin you still can log-in to Admin panel, "search users" and leaving the text field blank, press the button. It will show you all available users accounts where you can mouse over on some user and determine his ID, if it's necessary for adding a moderator, for example. In the same section you may search by username and find the associated user's ID even if this user still didn't posted any message (and so hovering the "member" title is not available).