Usually using a bench-top supply to power a known device that requires a fixed DC voltage is not much different from powering it from a wall-wart, except that you can limit the current to a more reasonable value in case of a short or circuit malfunction. This is very useful when the device is under development. A wrong connection or a short can burn out the device, so you'll need to replace it. The bench-top supply can usually save you this hassle.
To spell out an example, let's say I've made a simple circuit with a MCU and some other minor functionality (e.g. reading a sensor and reporting it via serial). I'll know that hethe MCU draws 1mA, the sensor is 15mA, so I can dial in 16mA as the limit. To have asome headroom, I'll typically useset more, e.g. 30mA.
When I turn on the circuit, if the supply says "16mA current draw", then it's all is fine. If it says 30mA, then itsit's "whoops, let's see what I've wired wrong".
If I used a 5V 1A wall-wart, and I've made an error, the device would possibly be fried before I can react.
As thece says, the current-limiting function of the bench-top supply can come in handy for other types of loads, like LEDs, lights, motors or batteries (you can use a bench supply to charge a battery, you have to be careful, but it's easily doable).