Depress means to lessen the activity or power of something. If you want to depress the spread of poverty, you need to find ways to slow it down, like by bringing education and skill-building resources into the poorest communities.
The word depress comes from the Old French word depresser, meaning "put down by force." Depress can be used literally to describe something you push down, like when you depress the handle on a toaster to lower the bread. It can also describe a more figurative lowering, such as the lowering of a person's emotional state. Attending a funeral is likely to depress you, and watching a sad movie afterwards will just sink your spirits even more.