Play mats have been around for decades. They are an area for your child to occupy while the youngster plays with their toys. The use in the home is not very common, but most daycares use them in some form. The mat will come in almost every texture, color, and shape imaginable, but their primary advantages and disadvantages are pretty much the same between them.
There are three major advantages to using a activity mats. The first is they create boundaries for your children. They learn that there are places to play and places that are for other things. The world is not one large playground. Used properly the child will collect the toys they want to use, bringing them to their play area, and not invade another child's play area. The second advantage is the mat itself is often a source of entertainment with colors, letters, numbers, and mazes on them. The last major advantage to the mat is it minimizes fights between children because they are staying to themselves which is especially helpful before naps or bed time.
The primary disadvantage to a play mat is cleanliness. By concentrating a child's play area you increase the germs, food, dust, etc in that area. If not sterilized properly you could increase illness. The other disadvantage is children who are already not social may use these as an escape from interaction with their playmates. You do not want children isolating themselves all day long. If you have this problem removes the play mat for some portions of the day.
Using play mats or not should not require a doctor degree in child psychology. Just use them appropriately and discourage children who actively break the play mat rule or runs to them for safety. Clean them everyday, and avoid fibrous mats because they wear quickly and are difficult to keep clean.