Caulk is the sealant. It comes in a tube and is used commonly by plumbers and carpenters trying to seal up cracks where air or water might push through. When a plumber caulks a tub, he's applying caulk to its seams to make it watertight.
Caulk can be used to describe both the process of applying caulk and the sealant itself. The word caulk comes from the Old Northern French cauquer, meaning "to press down." After you lay the caulk down over the seam you press it down by either running your finger over it or using a specific tool to force the caulk to settle into the hole you're trying to cover.