When you cover 1 end of the straw, atmospheric pressure, or air, can no longer get through the cover-straw interface/gap/crack to push the liquid towards the the other end of the straw. The surface tension and pressure of the liquid inside the half-closed straw also able to overcome gravitation force, so that the liquid stays in the half-closed straw even if you point the open end towards the ground.
On a side note, if you use a needle to introduce air back into the liquid (from the open air) then the air, with lesser density than most liquid, would go to the top of the half-closed straw. Its existence creates pressure inside the straw, and its volume will displace the same volume of the liquid, forcing that volume of liquid out of the half-closed straw.
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