To subsidize something is to support it by providing it with money or other resources. Don't expect your parents to subsidize your addiction to solid-gold puppy figurines.
We can break down the word subsidize to help us remember its meaning. The prefix sub- means "under, below" and sedēre means "to sit." (A submarine is a ship that goes under the sea.) So to subsidize is to underwrite something financially, providing the support that keeps it going. For example, our taxes are used by the government to subsidize many educational and social programs.