Sometimes, upgrades cost cookies, but can also cost hc or cps. As of version 2.052, there are 716 normal upgrades, and as of version 2.045, 13 debug upgrades.
Upgrades are things that make buildings and some other parts of the game better. For Heavenly Upgrades, see Ascension#Upgrade_Tree. For upgrades in beta versions of Cookie Clicker (if any), see Cookie Clicker Beta.