There are three possible Levels at which a Theme can be active: Site, Domain, and User:

Site

A Theme is set to be active at the Site level.

This means that everyone visiting the site sees it with that Theme.

Typical uses:

To speed up the styling of a site - style values stored in a theme can be shared across multiple style dialogs, making centralised changes easy.
To provide a choice of possible looks for a new site.

This is useful if the site can be visited at multiple domain names. For each domain name, you can set a different Theme to be active.

Typical uses:

If a business has several physical stores, give each store a sub-domain, and assign a different theme to each one. The theme can be used to control both the visuals (perhaps showing a picture of the respective store in the header graphics), and controlling content on some of the pages - for example the location details, opening hours, etc.
To provide different versions of a site - The theme choice can affect not just the visual appearance, but the content too, so could be used to provide versions of the site in different languages or stores in different currencies.

This is useful to allow individuals to choose the theme they want to use, without affecting others.

Typical uses:

To allow visually impaired users to choose a high contrast theme, or a theme with larger text.
To allow users to personalise their experience of a site (as an alternative to publishing different versions on different domain names). The theme choice can affect not just the visual appearance, but the content too, so could be used to provide versions of the site in different languages or stores in different currencies.
To allow a new theme to be developed, with the admin user experiencing it, before it is set 'live' at the Site level.