A yarn bowl, in its simplest form, is a flat-bottom enclosed-form bowl for holding one or more balls of yarn while they're being used for knitting and other knitting-like activities. Its purpose is to keep the yarn under control as it's being used. In most cases this also calls for a hole and/or groove in the side of the bowl to allow the yarn to be pulled thru. Ideally the bowl is also somewhat heavy so that pulling on the yarn doesn't cause the bowl to slide towards the knitter. The form is enclosed (top is narrowing than the widest inside point) to help keep the yarn within the bowl and not hop out over the side of the bowl. The bottom is rather wider than the standard “rule of 3rds” to increase drag/friction between the bowl bottom and the table on which it sits. Making the bowl from a heavy material also increases this friction to keep the bowl stationary.
Wooden yarn bowls must be sanded as smooth as reasonable, especially within the groove, to prevent snagging the yarn. A standard yarn groove is J-shaped so that the leading end of the yarn can be slide down thru the groove to be pulled out the tail of the J shape. One can also do spirals to reduce the chance of the yarn popping out of the groove as it is pulled upon and then becomes slack (at which point it could fall to the bottom of the J groove and pop out the long side on the next tug). Spirals do, however, take more time, require larger bowls, and are more prone to breakage than a simple J (since more wood is removed to make them).
Very large yarn bowls can hold multiple balls or skeins of yarn and thus can call for 2 or more grooves (preferably pointed in the same direction; i.e., one J and one backwards-J on the opposite side, so that both yarn leads can be pulled in the same direction; i.e., towards the knitter). These bowls are typically 9-10“ diameter or more.
Some knitters actually prefer yarn bowls without grooves and, honestly, when you have a very fancy and pretty bowl it can be tough to take a saw/drill/rasp to it and start carving grooves into its otherwise pristine sides.