Tags and segments are used to divide a subscriber list into parts that can be targeted by an email campaign.
Tags
Tags describe something about the user the tag is attached to.
Tags only need a name, that should describe what the tag says about a user. For example, a tag's name could be bought-product-A, which would be assigned to subscribers that have bought a certain item in your (web)shop. Users can be assigned multiple tags.
Tags can be assigned to users manually by clicking their email address in the subscriber list, or automatically when they subscribe through a form, read about this here.
Segments
A segment is a group of tags that can be targeted by an email campaign. An example of a segment could be bought-any-product or when using negative selectors have-not-bought-any-product.
When creating a campaign or automation, you can choose to send it to an entire mailing list, or one of its segments: