Marigolds are scented herbs of the genus Tagetes, and the ones in our gardens are mostly originally from Mexico, where they are known as caléndulas. About four Tagetes species are commonly cultivated, but untold numbers of hybrids, varieties and strains have been developed by horticulturists. The one pictured above is a "French Marigold" (from Mexico), Tagetes patula.
Since marigolds are members of the Composite Family, the blossoms you see above are actually clusters of many flowers. At the left you see a marigold I've split in half, showing disk flowers stacked in the center, with ray flowers at the side. At the right you see a ray flower on the left and the tubular disk flower on the right. In the picture at the top of the page, it's clear that the ray flowers comprise the reddish outside portion of the blossom, while the disk flowers make the yellow center. At the right, notice the Y-shaped stigma arising at the base of the flaring blade of the ray flower. The dark bottom of the ray flower is a mature fruit, or achene. The disk flower also has an achene, but it will mature and darken later.
One technical feature of marigolds is that at the top of the achene you find a pappus consisting of 3-10 unequal scales or bristles -- the white items atop the black achene at the left. The pappuses of some composites are stiff spines, or soft bristles, or low crowns, or nothing at all. These 3-10 unequal scales or bristles are important to notice if you want to be sure you really have a marigold.
Another typical technical feature of marigolds is apparent in the side view of the marigold at the top of this page. There you can see that beneath the colorful ray and disk flowers, there's a cuplike green thing composed of scaly involucral bracts. These green bracts have their edges united into a tube or cup. In most composites, the bracts overlap and are not connected.
So, if you see those unequal scales atop the achene, see how the green involucral bracts make a cup, and the plant has a pungent odor, and usually has opposite, pinnately dissected leaves -- you can be pretty sure you have a marigold!