Mulching is the number one thing to give your tree the boost it needs in difficult conditions, and otherwise is just a great idea for regular tree-care.
Mulch benefits:
maintains soil moisture by reducing evaporation — and the need for watering
acts like an insulating blanket, keeping soil warmer in winter and cooler in summer
improves soil aeration, structure, and drainage
inhibits certain plant diseases
protects the tree from humans — our feet compacting the soil, and our tools like lawnmowers and grass trimmers
However, too much mulch will stop gases exchange with soil; it can soak up too much moisture, not allowing water to percolate down to the roots; and if it is very near to the root collar of the tree, you can actually initiate crown rot.
So, mulch 2-4" deep, and keep a good 2" away from the stem of the tree.
Keep in mind that the root system of the tree is wider than most people imagine: the roots are typically 1-3 times the size of the canopy of the tree. Ideally, you want to fan the mulch out as far as possible to gain the most benefits (though that much mulch spread around the tree will look a little ridiculous, so find a happy medium).
Types of organic mulch include leaf litter, bark, wood chips, evergreen needles, and compost mixes.
You can also buy inorganic material (stone, rubber, geotextiles). Since they don’t decompose, you don’t need to maintain them. But at the same time, they don’t offer any nutrients or organic components, so the payoff is not nearly as great as organic mulch.