Ticklearmus is a spell that causes a hand to shoot from the casters wand tip and perform an action such as tickling or scraching. It is assumed the spell can be used for multible purposes, but in the books it was only used for scratching behind Lon's ear. The incantation is comprised of the words tickle arm us. The us is most likely added to the incantation to make it sound like a spell.
Barry used this spell to scratch Lon behind his ear in order to distract him so they could go for a walk.