When you do not put your finger on top of the straw opening, the air pressure on the liquid on all sides stays the same. When you do cover the opening, you trap some air in the straw. Since there is less air between liquid & blockage, the air pressure is lowered.
Putting your finger on top of a straw lowers the air pressure in the top (gas-filled) part of the straw. I know it is lower air pressure because the liquid stays. Same air pressure, the liquid would quickly fall out. Higher pressure would force it out, like bubbles in your milk.
|Higher in the straw||Water forced out|
|Lower in the straw||Water pushed up, defies gravity (however, gravity resists and the water slowly drips out)|
|Same in the straw||Gravity pulls water down|