Quoting the wikimedia documentation on this specific tool:
On Wikipedia, CheckUser is a tool allowed to be used by a small number of users who are permitted to examine user IP information and other server log data under certain circumstances, for the purposes of protecting Wikipedia against actual and potential disruption and abuse.
CheckUser itself simply produces log information for checking; it can require considerable skill and experience to investigate cases even with the tool.
Due to the mentioned access to IP data, the CheckUser privilege is only granted to a very small number of persons - on this wiki only the server admin and the manager.
Normally, CheckUser is only used in case of 'emergency' - e.g. bots spamming the wiki (so to ban a wider range of IPs from posting/accessing) or finding multi accounts if someone tried to push his own articles with different accounts.