This is, perhaps, the most ancient application of computers. A data processing center consists of a large number of computers that perform data processing (what else!) functions. These functions, however, have a large variation.
The more traditional data centers process data for government and commercial entities. For example, a data center may be responsible to compute and issue social security checks. Another data center may be responsible to process all monetary transfer operations for a bank.
More modern data centers include those run by national laboratories and major film production companies. With national laboratories, some data centers run particle and molecular simulations. In other words, large arrays of computer simulate the interaction amongst particles to model how real particles behave. Some laboratories also run nuclear explosion simulations to assess the effects of nuclear explosions with different parameters without actually detonating atomic bombs. Talk about environmentally friendly!
Film companies run powerful computer arrays for CGI (computer generated imagery). This is how we have all the films with realistic computer generated graphics.
Several properties characterize data processing centers: