The phrase "big shout" means making a loud and enthusiastic expression, usually to show support or appreciation for something or someone. Full definition
Big shout out to their defender who scored against us with his first goal in three years. (evertoniansclub.com)
Big shout out to all the other fabulous bloggers that were featured alongside me. (fashionablyidu.com)
Recipes from Cook's Illustrated and Antonella at Krumville Bake Shop in N.Y.C. both deserve big shout - outs for helping us develop this approach. (bonappetit.com)