Favorite decides whether you see that channel by default if favorited, or have to drop down the "X more channels" to get to it, but it also controls whether you get a notification (toast and badge icon) when someone @ mentions the channel itself.
Follow is basically subscribing you to get notifications for any and all activity in that specific channel. I reserve this for only the most important channels I have, as otherwise this can get VERY spammy very fast. I follow a channel that I will almost always drop everything to go see what is being said there. Some scenarios would be things like a critical incidents channel, or a Board of Directors channel, etc.
You must Favorite a channel before you can follow it.