Lawn aeration is good to do for several reasons. The resulting hole allows air and water to penetrate into the soil, you are actually increasing the surface area, and the plugs left on the surface to dry out allows the soil to interact with the thatch layer to break it down. With more air and water in the soil, turf roots will grow deeper into the soil and be much more drought and heat tolerant. The aerator should be a hollow tined type and penetrate into the soil 3 to 4 inches.
Core aeration is more often done in the late summer, just before fall growth resumes. If done in the spring, do not do it when the soil is really wet, as the aerator will leaves the sides of the hole slick and smooth, rather than rough.