A quarterly report is something that is carried out by companies four times a year, ie every quarter. These reports are made to give an overview of how the company's operations / finances are doing. It is designed to inform current owners as well as potential new owners.
These reports therefore contain important information about the company's financial condition and the company's health. It is then things like operating profit, equity, turnover, debt, etc. that are described. Bet is often also included notes and information that provide insight into the company's operations, business model and about their future plans.