The Canary Islands belong to Spain, which is a member of the European Union (EU). Like most other EU countries, then, the currency used in the Canary Islands is the euro.
You can easily pay for things while on holiday in the Canary Islands with your credit card, as well as use it to withdraw cash – and having a bit of cash on you can be useful if you visit any local tavernas or markets.
What's more is that Neilson resorts have a tab system in place so, if you buy something that's not included in your package, it'll be added to a bill which you can settle at any point during your stay.