Gudetama is a genderless character who's basically just an egg yolk—usually shown either lounging around on egg white or sitting in some Japanese dish. The character's whole thing is being lazy, and honestly, pretty depressed about it. Fans love Gudetama precisely because of that bleak energy.
The name plays on "gude gude," a Japanese expression for feeling worn out and lifeless, mixed with "tama" from tamago (egg).
Gudetama came into existence after Sanrio ran a contest to develop new characters based on Japanese food. The character placed second overall, losing out to KIRIMI-chan, a salmon fillet character who won instead.
Content compiled by AnimeList.moe from publicly available sources.