What could be interpret about the formation of a sedimentary rock from the information that its grains are, in the majority, fine and well rounded?

The fact that the grains are well rounded suggests that they have been subjected to a relatively high level of erosion (due to the smoothing of sharp edges). From this, we could interpret that the sediment has been transported a relatively large distance, providing more opportunity for erosion of the grains from abrasion, attrition, etc. In addition to this, the fine grains of the rock suggests the sediment was deposited in a low energy environment. This is suggested due to the fact that fine, light weight grains will not settle in higher energy environments as they are too light to settle if carried by stronger currents. They will therefore only be deposited when a low energy environment allows them to be deposited.