in my readings, spivak or elsewhere, i've come across this several times but i don't have the formal training (maturity) to know how to use it. intuitively: by the atlas maps on the manifold, we can chop up a manifold into patchs. for each patch, by smoothness or something, there is a smooth function whose (this is where i give up) support in nonzero. since these functions are nonzero on each patch and add up to unity, we can sum up these up over the entire manifold. is 'support of a function' an integrability contition that allows for nonzero terms in the sum like the characteristic function on a riemann integral?