a "claim" is an assertion of ownership (and also, more broadly, an assertion that something is true), so that ticket is your proof (assertion, statement, "claim") that you own your baggage.
In the early days of my country, there were mining towns that sprang up in un-owned land. People would "Stake a claim" by literally putting wooden stakes in the ground around the border of the property that they wanted to mine, and keep the profits from any gold or silver they found there.