I believe "claims" in this use, refers to what you "claim" the product can do. What you tell your customers that your product can do, must be true.
In other words, you can't sell water and claim it will cure all illnesses.
ISO 9001 - Clause 8.2.2 - Determining the requirements related to products and services
b) the organization can meet the claims for the products and services it offers.
Claims = Requirements ?
Jelly
Explanation in ISO/TS 9002:2016 for »claim« is as follows:
"The organization needs to ensure it meets the claims for the products and services it offers. A claim is a statement by the organization about its products and services and their features and characteristics that it can provide to customers. For example an internet service provider (ISP) might make claims about download speeds on its website; a manufacturer of laptop computers might make claims about battery life in a brochure; a car manufacturer makes claims about fuel economy in an advertisement; or an insurance company says it provides a 24 hour claims service."