Potemayo is a cute, surreal comedy where weird little critters resembling baby furries appear randomly one day, and ordinary schoolkids end up having to figure out how to care for them. It's similar to Pokemon, Digimon, and the like, but it doesn't have the epic action shounen feel these "cute monster taming" shows usually have. Instead of fighting, the focus is on peacefully resolving conflicts and on nurturing these strange little creatures. In that regard, it is kind of similar to the Lilo and Stitch cartoon, where the characters aim to help the monster critters understand and be understood.
The show gets its name from the main creature, Potemayo. She is so named because the protagonist, a boy named Sunao, finds her in his fridge one day, eating a bun with potatoes and mayonnaise. He gives her the name Potemayo as a portmanteau of "potatoes" and "mayonnaise". She is adorable, but very feisty. Much like a Pokemon, Potemayo does not talk, but speaks the same syllables over and over again (but not her name, unlike a Pokemon). Sunao has to figure out how to deal with Potemayo, take care of her, keep her happy, and deal with conflicts and messes she causes. Later, creatures like her show up, including a fierce, antagonistic one called Guchuko, who does not like people.
Manga by Haruka Ogataya
Basically, the show has two things going for it; comedy and the mystery surrounding Potemayo and the others like her. What are they? Where did they come from? Why are they so darn adorable? I'm not sure, after watching episodes 1-5, that these questions arising from the initial viewing will be answered necessarily, since the anime is only 12 episodes long total. The original manga was in the "4 panel joke" format, so the focus of this anime is definitely on comedy. However, I worry that that means the anime sacrifices making sense and giving enough exposition for the sake of being humorous.
So, if you like cute chibi furries doing cute things (think DiGi Charat but with a less annoying main character), this is one to watch. It also has some good, old fashioned style school comedy, like stuff from an old sitcom. Since the manga in both are 4-panel comedy manga, the humor in this one is similar to Azumanga Daioh!, and I would recommend this for fans of that type of comedy. Personally though, it's not my thing, but that's just a matter of personal taste. It's good for what it is, a sweet, fluffy, relaxing comedy where you will not have to think too hard.