They are a tribute to sprites of 8-bit video games. They are very simplistic-looking, made up of large pixel blocks.
How to Obtain
8-Bit style petpets are only available from the Petpet Lab Ray and an 8-bit Power-Up Potion.
Some 8-Bit pets come with removable clothing as part of the colour. However, regular clothing can not be used on an 8-bit pet, with the exception of background items, foreground items and trinkets.
Notably, 8-Bit Staff cannot be worn due to the fact that it is a held item.
Here are all the neopets that can be painted 8-bit.
Here are all the petpets that can be painted 8-bit.