Tuning serves many functions, some aesthetic, others functional. Let’s start with the aesthetic.
The harp makes a beautiful warm rich sound that we enjoy. Tuning is one of the many elements of achieving that tone. If your strings are not each in tune, the sound of each string will “fight” with the sounds of the other strings. This is not pleasant to hear. Even being off by a hair (as indicated by the needle and lights on your tuner) will be noticeable. And the more off your strings, the easier it is to detect that you’re not in tune. And of course, you will instantly sound better if you are in tune!
We habitually tune to an A of 440Hz. This is a convention - you can tune to any frequency you choose (e.g., Highland pipers tune A to about 470 - which is just about our Bb!). We elect to tune to A440 (just like a lot of other instruments) which allows us to come together as a group and play (or to play with other instruments). Be sure to check that your tuner is calibrated to A440 or you’ll be in for a nasty surprise!