It means that you're strong. Takes a licking, in slang, means being beaten up. Keeps on ticking means that you keep on going. So, it means that you keep on going even when you're being beaten up.

kim, "to lick someone" means to defeat someone in a fight "a licking" is a beating or sound defeat. "It takes a lickin and keeps on tickin!" is the advertising slogan for Timex brand watches. It means that Times watches can suffer a beating (a lot of damage) and keep working (ticking).

take a licking = take a beating keep on ticking = keep on living When an animal has been wounded, it licks itself. Hence the expression. When you are alive, your heart is ticking. Hence the expression. Geddit?