Early computers could compute significantly faster than any room full of humans, and do so more accurately.
Before electronic computers, calculations and computations were handled by people ("computers"), often women, crunching numbers in a room on paper (perhaps aided by mechanical calculators in part, depending on the era). This was a slow process, as you can imagine, involving a lot of people, a lot of paper and a lot of time. Anything that required large-scale calculation had to be handled this way, from cracking codes and calculating trajectories of weapons, to dealing with statistics and payroll. Some calculations were just too mind-bogglingly slow to be worth attempting with humans and mechanical aids. Computers in the 1940s and 1950s did this kind of computational work that would either be expensive with regards to the amount of humans that would have to be employed to do the work, to reduce errors, or simply to make the work fast enough to be useful.
For example, the UNIVAC I was famously used to predict Eisenhower's win in 1952, after being fed a small percentage of data, before all the votes were officially counted. This was work that couldn't be done fast enough by people in the time available but could be completed by machine.
Because of the expense of computers, the only institutions that could afford and use computers were large and wealthy, and of course requiring large-scale calculators. It's not surprise that the first UNIVAC I's sold were sold to the US government (census, military applications), research facilities (nuclear and radiation research) and to major corporations such as GE.