He came to count. Count von Count was his name. Probably some distant relative of the infamous Count Dracula, the Count of Sesame Street shared the iconic voice made famous by Bela Lugosi. His original puppeteer Jerry Nelson was feeling particularly clever one day and presented this new character to Jim Henson. He loved the idea of a count whose sole purpose was to teach counting. But it's not as if he had any choice. It was all the purple man could do.
(Thanks to the humorous "censored" version of the song, the original can not be uploaded. But you can watch it here.)
The Count's love of counting is not completely based on the pun in his name, however. It can be traced to a an actual affliction that many suffer from. Arithmomania is a specific type of obsessive-complusive disorder that manifests itself in a need to count something, either out loud or in one's head. Sometimes it can be mild and harmless, such as counting steps as you go up them, and once the counting is over, it has no further effect on the counter's life. But sometimes, the need to count is so strong, that the counter will feel uneasy or convinced that danger will result if the counting is not completed. This can result in the afflicted person repeating tasks (like turning a light switch off) multiple times, making sure the task was done "properly" and the "correct number of times." Other times, people or objects are assigned numerical values so as to organize everything in the victim's mind.
Somehow, in ancient Eurpoean folklore involving vampires, these creatures were thought to suffer from arithmomania. If being pursued by a vampire, one could escape by throwing a handful of rice or seeds so that the pursuer is compelled to stop and count them all. As a precaution, graves of those believed to have the potential to become a vampire were surrounded with grain and seeds so that the newly undead being could not travel very far.
Count von Count possesses this quality to such an extreme that he posits no threat to anyone on Sesame Street. There are an infinite number of things to count, and he is easily distracted by any of them. Although he has the fangs and attributes of a potential blood-drinker, his weakness prevents him from causing any harm.
But he can cause a lot of annoyance. As seen in the following parody of The Rocky Horror Picture Show, the Count's disorder prevents them from getting past the first scene.
This is one monster who is cursed to live an afterlife with his internal demons. At least he is using his ability for the good of mankind, instructing today's toddlers how to count and not making them his zombie slaves. And, despite his exaggerated problems, he is still the best vampire role model we have at this current time.