Learn Italian: Questi stivali costano troppo; in quel negozio ne vendono di robusti. - These boots cost too much; in that store they sell some sturdy ones.

When using the pronoun ne (meaning "of them") alongside an adjective to mean "some [adjective] ones", you must place the preposition di right before the adjective. Without di, saying ne vendono robusti would be grammatically incorrect.

What exactly is ne replacing in this sentence?

ne is replacing the idea of "some boots" (degli stivali). Instead of repeating the noun and saying in quel negozio vendono degli stivali robusti (in that store they sell some sturdy boots), we use ne to efficiently say "they sell some sturdy ones".

Could I just say vendono alcuni robusti instead?

No. While English lets you say "some sturdy ones", Italian doesn't let you use alcuni directly with a standalone adjective like that. If you drop the noun, you must use the ne ... di + adjective structure we see here.

Why does robusti end in -i if the noun it describes is missing?

Even though the noun is replaced by ne, the adjective must still agree in gender and number with the noun it logically refers to. Since stivali (boots) is masculine plural, the adjective must be masculine plural (robusti).