When a domain is available, anyone can register it and claim it as their own. You (or anyone) can register the domain from an accredited domain register for your own personal or business use.
Depending on the TLD of the domain (the part after the last “.”, for example, .com or .net), there may be additional restrictions on registration. This is common with country or profession based domain TLDs, such as .ca, .uk or .lawyer.
A domain will remain in this status until someone registers it.