What is the process by which plants lose water through leaves?

Transpiration, and it is not really a loss so much as an engine. Water evaporating from leaf surfaces pulls on the water beneath it, and because water molecules stick to each other, that pull travels down unbroken columns through the whole plant - drawing water up from the roots against gravity with no pump involved anywhere.

That is how a hundred-metre tree drinks. The tension in those columns is enormous, and it is also the reason there is a height limit for trees at around 120 metres: above that the tension required would tear the water columns apart. Measurements on the tallest redwoods show the topmost leaves already water-stressed and shaped differently from those lower down.

The cost is that a plant must open pores in its leaves to take in carbon dioxide, and water escapes through the same holes. That trade-off governs plant life everywhere - which is why desert plants open their stomata only at night and store the carbon dioxide until morning, and why a large tree can move hundreds of litres of water a day into the air. Forests generate their own rainfall this way, which is what the Amazon's flying rivers are.