There are a couple of common beliefs for this gesture. Literally crossing your fingers is a hand gesture and is made by crossing your index and middle finger around each other. The two most common beliefs are: 1.) as a gesture for good luck; for wishing good luck. A friend may be going into a job interview and may ask "Please cross your fingers!" and so they are asking for you to wish them good luck. 2.) As an excuse to tell a white lie. ---this is common amongst children. An example may be if a parent asks their child "Did you do your homework" and the child responds "Yes." but during their response they have their fingers crossed they are actually lying. And when the parent finds out they were lying the child may say "I had my fingers crossed!" as an excuse for their lie. I know. None of it makes sense. :)

The first thought in my mind is, "for a lucky outcome". It Gives You Good Luck! https://www.youtube.com/watch?v=KGsfxkCmHvo

I agree with the meanings given below but the phrase should be "Fingers Crossed" not "Fingers Crossing", at least in American English.