After-dribble means the loss of a few drops of urine. This is usually after leaving the toilet. The medical term for this condition is post micturition dribbling (PMD).
This page gives you information about PMD and how to manage the condition.
Few men admit to having this problem but a great many suffer and are embarrassed by it. PMD affects men of all ages. It usually happens just as the penis is being replaced and garments rearranged - then the trousers get wet and stained.