What a challenge is
On a ladder, you play the people above you. A challenge is you asking one of them for a match - and while it is open, neither of you can be challenged by anybody else, so nobody ends up owing three matches at once.
How far up you may reach is your club's decision. Some clubs allow one place, some allow three. The screen tells you who is within reach when you make one.
The versus screen
Every challenge has a page of its own, with both of you on it: where you each stand on the ladder, how far apart that is, and what has happened between the two of you before.
It is meant to be sent. There is a link on the page and a button that copies it, and whoever opens it needs no account - send it to the people you want watching.
It keeps working afterwards
The link does not expire when the match is played. People open it again to see who won, which is half the point of having sent it.
If you were challenged
Whoever runs the section records the result once you have played. Until then the challenge sits on your dashboard under the things waiting on you, and tapping it opens the versus screen.
If you cannot play in time
Tell whoever runs the section. A challenge that is never answered lapses on its own after your club's window, and lapsing is not a loss - nothing is recorded against either of you.