It's like wearing a T-Shirt but you get the added benefits of have strong BDU sleeves for crawling and protecting from thorns and debris.
DriFire fabric is the standard body fabric in Crye and USMC FROG shirts; it's just like t-shirt material but fire resistant and dries faster.
Massif, New Balance, and some other name brands use a soft mesh fabric as part of the body. My experiences are mixed on those.
The off brands and clones you want to be very careful with body fabric. Some are made of mostly cotton, but there are some made of 100% polyester and other synthetic stretch/compression fabrics; these synthetics may not breath or dry very good and increase heat problems. I've had good experiences with the 100% and 50%+ cotton blends but they don't holdup as well as the name brands and fade significantly faster. I've had very bad experiences with the synthetics.
The BDU sleeves are not like they used to be in the old days, you actually have some choices now. You can still get the strong and proven 50/50 Nyco Nylon/cotton blend but theres a newer 70/30 blend that has been very popular. Highline brands like New Balance use very complicated fabric blends that are generally softer twill types. Offbrand/clones use a variety of things from 100% cotton ripstop, 100% nylon ripstop, normal cotton twill, etc etc; usually these fade much faster and get torn relatively easy compared to name brands. My 2 cents.