What is tag mode in Animal Crossing?

Answer 1

Tag mode is an option you can click at the title screen.

To do tag mode, you need to buy a note in a bottle and release it in the ocean AT THE SAME TIME another person you know is.

Then, you both click on Tag Mode, and the letters will arrive at each other's towns.

(This is a great way to send presents to your friends without having to visit each other's towns.)