Tags allow you to filter the recipients of a message, meaning your message only goes to those recipients who have all of the selected tags.
For example, I've set up my Omnilert for a school and have three possible tags for "Students", "Faculty", and "Staff". This means I can target each of those roles within my various groups (I've set up my "groups" to represent my various campus locations).
However, if I send a message with the tags "Faculty" and "Staff" selected, my message will only go to those subscribers who have both tags.
In this case, I only reach my subscribers who have both the "Faculty" and "Staff" tags.