When you turn down an invitation, that's a declination. Another kind of declination is when something slopes down, like the declination of a playground slide.
Look at the noun declination and you can see the verb decline, which means "to lessen," "to slope down," and "to refuse." Declination is the process of doing any of these things. In astronomy, it's also the distance between an object and the celestial equator, measured at an angle. The Latin root is declinatio, "a bending away."