decline
To politely say no to something offered to you.
Decline means to politely refuse something, or to gradually become worse or weaker.
When you decline an invitation to a party because you have other plans, you're saying “no thank you” in a respectful way. You might decline a second helping of dessert, or decline an offer to play on a sports team. The word suggests courtesy: declining isn't rude or abrupt, it's a gracious way of turning something down.
The word also describes something getting worse over time. A student's grades might decline if they stop studying, dropping from A's to C's over several months. An athlete's performance can decline with age or injury. Ancient Rome went through a long period of decline before it finally fell. When doctors talk about a patient's declining health, they mean the person is gradually getting sicker.
In both meanings, notice the sense of downward movement: you're turning down an offer, or something is heading down from a better state. The noun form is a decline, as in “a decline in test scores” or “the decline of the Roman Empire.”
When something is described as being in decline or on the decline, it's losing strength, quality, or importance. This could apply to anything from a civilization to a business to someone's enthusiasm for a hobby they used to love.