The theme tags are used to sort/categorize themes in the WordPress theme directory according to features or characteristics.
For example, if your theme supports two columns (a typical blog format), then you use the two-columns tag and if it supports multiple screen sizes, use the responsive-layout tag. This makes it easier for someone looking for a theme to be very specific – i.e. “I want a theme which has three columns, mainly dark colors, allows for big featured images and supports the Arabic language. And it should work on all devices including phones and tablets.” This would translate to a tag list like this: three-columns, dark, featured-images, rtl-language-support, responsive-layout.
These tags are only used on the WordPress theme site and are completely optional. However, it means that people using those search filters might not find your theme and that’s no good. If you’re making a custom theme for yourself or for a client and you’re not going to upload it to the WordPress theme directory, you don’t need to include them.
For a full list of tags you can use, check https://make.wordpress.org/themes/handbook/review/required/theme-tags/.