Why does a matchstick burning in a container cause suction?
When the container is open to the atmosphere and has the match burning in it, the temperature of the air inside is higher than the temperature of the surrounding air.  In order for pressure to be equal in the container and outside it, the density of the air in the container is less.  When the match is removed and the container placed on the person, two things happen.  One, no air can enter or leave the container, and two, the air in the container begins to cool.  When the air in the container cools its pressure drops.  The atmosphere pushes on the air in the container indirectly through the person, creating what is called suction.

This is similar to drinking through a straw.  You are not sucking the liquid through the straw as much as you are removing the opposing force that prevents the atmosphere from forcing the liquid through the straw.  The opposing force being the air pressure in the straw.