Character Pool is where you put your created soldiers (or your game's randomly generated soldiers). As these soldiers get promoted (level-up), they can be customized to your heart's content. And with cosmetic mods, the customization of these soldiers should be infinite. That is why the developers created a way to save these soldiers appearance, stats, and whatever you did to your soldiers so that you can share them with your friends.
All you have to do is to save the character in the Character Pool in-game. You can find the characters in this location:
[Drive]:\Users\[Username]\Documents\my games\XCOM2\XComGame\CharacterPool\Importable
Your best bet is sending these characters via email. The next one is to upload the files to a cloud service site like Dropbox, Google Drive, and others. Be careful though not to give access to your entire cloud account. These cloud services have options to only send the specific file instead of gaining access to the entire folder.
Skype and other chat programs that support file transfer is also fine.