A gambling licence binds the company that holds it to a set of rules: checks on the identity and age of players, tools for limiting play, fair handling of complaints and regular reporting to the authority. Breaking them can bring fines, conditions or the loss of the licence. What the licence does not do is guarantee a pleasant experience, and the strength of the rules varies a great deal between one authority and the next.
Casino sites often run on a platform owned by another company, which holds the licence on their behalf. The terms should name that company and its registered address, and the name should match the register exactly. It is normal for several sites to share one licence; a site whose terms name one company while the footer shows another company's number deserves a question to support, answered in writing, before any money moves.
Every licensing authority keeps a public register of the companies it licenses. Searching it by the licence number or the company name shown on the casino site should return a single entry, with the same company, an active status and, on many registers, a list of approved domains. A number that returns nothing, a different company or a domain missing from the list is a reason to stop before depositing anything.