There are five types of tags:
- Easy (1): This thing appears on easy mode.
- Medium (2): This thing appears on medium.
- Hard (4): This thing ap… well, you can guess it.
- Deaf (8): Various effects, depending on the thing. For monitors, it makes them randomly respawn in Match mode. For pushables, this makes them non-pushable. For rings, this makes them float, giving them a more natural look. For other things, it may have other effects. Their respective wiki articles will tell of what they are.
- Multiplayer (16): It has to do with whether it appears in multiplayer, though I myself am uncertain what specific modes it pertains to.
The tags number is a sum of all the applicable tags, and may range from 0-31. For example, a monitor that appears on any difficulty and does not respawn randomly in match mode would be 7 (1+2+4). A ring that appears only on Easy and floats would be 9 (1+8).
For checkpoints, tags serve a different purpose entirely. They behave the same way no matter what the tags value is. However, the order of the checkpoints depends on their tag value. The first checkpoint in a level (or race) would be 0, the second would be 1, et cetera. Activating a checkpoint will activate all previous checkpoints (that is, checkpoints with a lower flags value than itself).
At least, this is as far as my understanding of it reaches.