When you save a card to your Wallet, like a pass for public transit, a card for Apple Pay, or the key for your car, it's saved to something Apple calls the Secure Enclave. It's where your iPhone saves all of the important things that need the utmost security and your cards fall into that category for obvious reasons. But while it's no surprise that the Secure Enclave has a finite amount of space in which to save things, you might not be aware that it's actually possible to reach the point where that space is full and the only way to fix that problem is to delete some cards.
What's more, the Wallet app will not allow you to add any more cards until after you make some space and that means that you might have to make some difficult decisions about which cards you need, and which you don't. I'd suggest keeping the card that unlocks your house or car and ditching the supermarket loyalty card, but the decision is yours.
