Learn German: Du brauchst Bargeld, falls du einkaufen willst. - You need cash in case you want to go shopping.

Because falls is a subordinating conjunction. It introduces a dependent clause, which forces the conjugated verb (willst) to move to the very end of that clause.

Could I use wenn instead of falls here?

Yes, you could say ... wenn du einkaufen willst. Both words can mean "if," but falls specifically means "in case" or "in the event that." It makes the condition sound a bit more hypothetical, emphasizing that it is just a possibility that you might go shopping.

Why is the order einkaufen willst and not willst einkaufen in the second half?

In a normal main clause with a modal verb, the conjugated modal is in the second position and the infinitive goes to the end (Du willst einkaufen). However, because falls pushes the conjugated verb to the absolute end of the clause, willst has to jump right past the infinitive einkaufen.

What happens to the word order if I start the sentence with the falls clause?

If you put the falls clause first (Falls du einkaufen willst, ...), that entire clause counts as the first position of your overall sentence. To keep the main verb in the strict second position, you must immediately follow the comma with the verb: ... brauchst du Bargeld.