Backhoes have been around more than 40 years, and they've gotten even more popular in the last decade. Caterpillar has been manufacturing Backhoes since 1985. The main reason we see Backhoes at work all the time is that digging and moving dirt is a big part of a lot of different projects. For example, you need to dig ditches to lay pipes and underground cable, set up foundations for buildings and create drainage systems. There are a number of tools that do this sort of work, often more efficiently than a Backhoe, but many construction crews use a Backhoe instead because of a number of factors.
For one thing, Backhoes are compact when compared to large, specialized equipment such as Excavators. They can move around all sorts of construction sites and you can take them on the road. Mini-loaders and Backhoe units are actually smaller than a typical Backhoe Loader, but if a contractor needs to dig and load, it's usually better to have both units in one. It saves a lot of time because the operator doesn't have to switch between two different pieces of equipment.
The Backhoe and Loader components don't have quite as much power as larger equipment, but they do very well, even with fairly difficult jobs.
A construction crew that does all sorts of different work will usually buy a Backhoe rather than more efficient specialized equipment because the Backhoe performs well in a wide variety of situations.