The answer to this question can vary depending on who you ask. If they have sat on a mesh chair before, they will most likely give you their personal opinion - which while fine, is not the ergonomic answer to whether a mesh chair is any good or not.
There are three types of mesh chairs - those with mesh back and seat, like the infamous Herman Miller Aeron, those with a mesh back and leather seat, and those with a mesh back and foam seat. Here are some of our mesh back chairs with mesh seats. The most important thing to understand about these chairs is that the mesh is going to be springy, almost bouncy, since you are in fact sitting on air. The benefits of these types of seats are debatable, but they are not un-ergonomic, nor exude the principles of a great ergonomic seat. The mesh is a little less harsh on your thigh's circulatory veins than your standard foam, because of the "springy" factor, however, mesh is not as supportive as foam, for the same reason. We recommend a combination of mesh back and foam or leather seat such as these chairs, for example), where you are getting the best of both worlds - the breathability of Mesh on your back, and the support and comfort of a foam seat pad.
Of course, that is our opinion. There are those whose absolutely swear by a mesh seat, there is absolutely nothing wrong with that.