In cooking, the word dredge means to coat an item of food in flour or breadcrumbs before cooking it.
Dredging with flour is often one of the steps in the standard breading procedure, which is a preliminary to sautéeing or deep-frying.
For example, dredging chicken in flour is one of the steps when preparing chicken piccata (likewise veal piccata). Croquettes or cutlets are also usually dredged with flour before cooking.
Dredging in flour requires the item to have some moisture about it, which is the case with most food items.
The standard breading technique involves first dredging the item with flour, then dipping it in egg wash, and then finally coating it with breadcrumbs. This works because the flour sticks to the food, the egg sticks to the flour and the breadcrumbs stick to the egg.
You'd usually add some sort of seasoning to the flour and/or breadcrumbs. Salt and pepper are pretty much a given, and paprika, chili powder, garlic powder and dried or fresh herbs are also good candidates.
It's a good idea to shake off any excess flour so that the coating doesn't turn pasty or gummy.