There are several expressions involving the words "against the/a wall" - such as "banging your head against a wall" and "having your back against the wall"; but I can't remember seeing or hearing the words you quote used as an idiom. Perhaps they mean precisely what they say - ie to throw a lot of things at a wall. If you're still.puzzled, it might help if you provided the context in which you read or heard the words.
I can't tell you what it means by try looking on this site http://www.snopes.com
it's basically an urban legend site so any phrases, old wives tales, rogue stories you've heard you can look them up here and it'll tell you where they orginiated from and if they're true or not.
Its saying something like, lets look at everything and see whats important. Throw mud on a wall and only the best thickest will stick, rest will run down.
"throw (whatever) against the wall and see if it sticks" To see if something is doable or agreeable. (Similar to "run it up the flagpole and see if anyone salutes") Probably has its origin in cooking - many chefs believe that the best way to see if pasta is properly cooked is to throw a strand of it against the wall (or a hard surface) and see if it sticks.