Example 1: I have been training for the Los Angeles Marathon for 6 months and the race is coming up in a couple of weeks. I’m prepared for the run, but I’m nervous because the weather report shows rain for marathon day! It’s such a big event with a lot of preparation by the city so it will happen come rain or shine. I really hope we have nice weather that day. Running in the rain would be dreadful.

Example 2: 
Maggie: Hi Jessica! How are you? 
Jessica: Hi! I’m great, thanks! I’m pretty excited for my wedding this weekend!
M: Wow that is exciting! I hope the weather stays clear and sunny for your big day.
J: I hope so, too. but I’m not worried! I know everything will be perfect rain or shine!

Meaning: (come) rain or shine = no matter what the weather or situation (usually weather). In Example 1, the Los Angeles Marathon will not be cancelled if it rains on that day. In Example 2, Jessica says she expects everything will be fine even if it rains. 

This expression can be used with come without changing the meaning. Example: We will be there come rain or shine. = We will be there rain or shine.