Ir de... + noun is a pattern that you can use with a number of nouns. The meaning is about the same as the English "to go ...-ing". It has a connotation of planning or intent.
The word compra is a noun that means "purchase", "an act of buying". Ir de compras means "to go shopping", "to go on a shopping tour". It's in the plural because you'll probably shop for several items, and also because that's just how the phrase is used (it's a fixed idiom).
Other examples of this pattern:
- ir de paseo = "to go for a walk" (or "to go for a ride", if in a vehicle)
- ir de visita = "to go visiting", "to go on a visit" (ir de visita a lo de alguien = "to go on a visit to someone's house")
- ir de viaje = "to go on a trip"
- ir de copas = "to go out for drinks" (copas = "cups", figurative for "drinks")
For most of these you can use the verb in its pronominal form, with the "reflexive" pronoun: irse de compras, irse de viaje, etc., but not when speaking of habitual actions.
Me voy de compras. ¿Necesitas algo?
"I'm going shopping. Do you need anything?"
Generalmente voy de compras los sábados.
"I normally go shopping on Saturday."
Voy a comprar todos los sábados sounds wrong, mostly because comprar likes to have a direct object (the things that you're buying). Voy de compras solves this and allows you to be more general: you don't need to specify what you're buying, just that you're out shopping.
Finally, for many of these verbs you can replace ir with salir, with an almost identical meaning:
- salir de paseo = "to go out for a walk"
- salir de viaje = "to go on a trip"
The idea is the same, with the added connotation of "going out" (implying absence and distance).