To understand serfdom, one must think in terms of property law. There are two kinds of property - moveable property also called chattels, and immovable property also called messuages. Think about when you sell a home and move to a new one. You take your chattels - your clothes, furniture, car, etc - with you, but you leave the messuages - the land, the house, the sidewalks, the trees and bushes, the fences, etc. - behind. A slave was a chattel but a serf was a messuage. In the eyes of the law the serf was legally bound to the soil just as if he or she was a tree or a building. If land transferred from one landlord to another, the serfs also transferred to the new lord.
There were certainly barbarian antecedents to this practice, like Jean said, but there were also Roman antecedents. In the late empire landlords often found it difficult to retain farm labor. City life was much too alluring. So laws were made that tied peasants to the land. Land became valuable not only for its own productive capacity but also because it came with a labor force already in place.
Many first-generation serfs had perhaps been slaves so becoming a serf was actually an improvement. Other first-time serfs had perhaps been dispossessed of their land so again, becoming legally bound to the soil meant that one could not be dispossessed again. Landlords preferred serfdom over slavery because slaves have to be supervised and driven to maximize their productivity, but serfs were self motivated since the serf got to keep everything over and above the rent that he paid to the landlord.
There were at least two kinds of rent. As Jean said, it was usually paid in kind, not cash. The lord usually took a portion of the serf's harvest, similar to sharecropping. Fixed rate was to the advantage of the landlord. It provided the lord with a steady income regardless of the quantity of the harvest. Percentage rate was usually to the advantage of the serf since in bad years he paid a lower rent and in good years he could afford to pay higher rent.