When you turn over the jar and the index card stays without water pouring out, that is caused by Atmospheric pressure. Atmospheric pressure is the force that holds the index card in place. The card stays on the upside-down jar because the pressure of the air molecules pushing up on the card is greater than the weight of the water pushing down.
When you remove the index card the water stays in the jar because of surface tension. The molecules of water are joined together to form a thin membrane between each tiny opening in the screen.
When you tip the jar, air will come into the jar and break the seal, causing the water to pour out. If you return the jar to its upright position, the air can no longer go out and the water will stay inside the jar.
Toothpicks go through the screen and let just a little water out but doesn’t break the surface tension.