Mosquitoes need to lay their eggs shortly after receiving a blood meal.
This blood meal is the future food supply for her larvae. After biting someone or some animal she is compelled to seek stagnant water in which to lay her eggs. Evolution has taught her how to identify stagnant water (low oxygen) because running water will just wash all of her eggs away. She needs water that sits so that her eggs are protected from rolling. The larvae use little snorkels that stick out of the water in order to breathe. Running water can roll the larvae over, filling the snorkels and causing them to drown.
The way she finds stagnant water is by detecting the water molecules of as they move through the air, then detecting the lack of oxygen molecules coming from it. She has learned over thousands of generations to follow these molecules back to their source. The water does not have to be fouled or bacteria laden as in a swamp, it just needs to have low oxygen levels.
What the Lebost-Evarcha trap does is provide a simple reservoir of water with the oxygen removed to attract the mosquito. A sticky net, like a spider's web is then used to catch her before she can lay her eggs then go off to bite another person- effectively breaking the chain of spreading disease.