When God speaks of a covenant with the Israelites in Exodus 19–20 (or anywhere else in the Bible), he is making a deal with them. A covenant is a contract or a bargain. It is saying, "if you do something for me, then I will do something for you." It is reciprocal, for each side has obligations.
God first tells Moses, in Exodus 19, that the following is his offer (when God says "you" below, he means the plural "you" of the entire Israelite population):
Now if you obey me fully and keep my covenant, then out of all nations you will be my treasured possession.
In chapter 20, God fleshes out what his covenant or contract is: he wants the Israelites to agree to obey the Ten Commandments. If they do so, he will treasure, bless, and protect them as his specially chosen people.
Huston Smith, a scholar of comparative religion, understands this idea of covenant as a departure from earlier religious practices because it is based not on the whim or caprice of the gods, but on a rational plan that trades God's blessing for ethical behavior. In pagan religions, gods needed to be appeased, but this was done usually through burnt offerings or other gifts meant to keep them happy so that humans could stay fortunate. As long as the person in question made the proper offerings, they were considered to be "fine" with the gods; ethical behavior was not necessarily part of the deal. Ethical behavior was honored in pagan cultures, but it was not integral to the practice of religious faith. With Judaism, ethical behavior became the core way to please God.