The valves are an essential feature of the heart because they prevent backflow. Think of them as one-way doors, or turnstiles.
The heart is a muscle, and the entire circulatory system functions on the basis of the heart contracting and relaxing, thereby decreasing or expanding the volumes of its various chambers. When the heart contracts and decreases volume, this increases the pressure on any blood contained in that particular chamber, increasing the flow of that blood out of any available exit, such as a valve or an artery. However, once the heart relaxes, the volume of that same chamber increases, causing the pressure to decrease and thereby drawing blood in.
If the heart didn't have some way of moving blood from point A to B, and then preventing it from going back into the chamber it just came from, then the heart's contractions would be almost pointless and most of the blood would simply slosh around in the same place. You can observe this effect by holding something like a water bottle under the sink, and squeezing it repeatedly to see the water simply flowing in and out.
The tricuspid and bicuspid valves are the valves that are situated between the right and left atria, respectively, and regulate the flow of blood out of those regions and into the corresponding ventricles.