Why Do Trees Shed Their Leaves?

Shedding leaves is a plant's equivalent of hibernation. During warm spring and summer days, there is plenty of sunlight and water to carry out photosynthesis. Photosynthesis is a process by which plants take up carbon dioxide and water and convert them into glucose and oxygen. They need sunlight to drive this reaction. In winters, there is little sunlight. That means that little photosynthesis is able to occur. Less photosynthesis means less glucose. Glucose is the compound that provides energy to plants to live and grow and is also important for the manufacture of the structure of plants as it can be converted into proteins, cellulose etc.
Imagine if you had no food, would you still want to play ball for an hour? You would rather not because that would make you hungry and eventually undernourished and starved. So, you would most probably stay indoors and do nothing. You are conserving your energy in this way. Similarly, plants need to minimize their energy use in winters because there is no food (glucose). So, they shed leaves to reduce the maintenance energy. They do not grow or reproduce during this time as they are conserving energy.
There is also another reason for shedding leaves. If a leaf stays on the branch for a very long time, it is at a higher risk of infection and disease. So, every winter leaves are shed and in spring new ones grow out.
However, you should also know (and you probably already would) that not all leaves shed their leaves in winters. Only the deciduous trees lose them in autumn. Evergreen trees like conifers do not lose their leaves/needles but maintain their foliage throughout the year.