In Italy, they call it 'soffritto', in France it's 'mirepoix'.
Simply onion, carrot, and celery, chopped and started as a flavour base for soups, and sauces, casseroles, and stews, is something my mother would never dream of not doing. I call them 'the flavourers', because that's what they do!
Now if you want to get all nit-picky, in Italy they sweat these three wonder ingredients off in olive oil, and in France they use butter. I think the correct proportion is 2:1:1 of onion, carrot and celery, but hey, I'm not that concerned! I'm cooking for my family, not a three hat restaurant.
If you are stuck without celery, you can use parsnip, or fennel....it won't be the same, but it does add that extra dimension that seems to complement the carrot and onion.
And, it goes without saying....garlic! ooh..and wine, herbs...you get the picture!? Flavour, flavour, flavour...not a need to buy a 'Contintental' flavour base packet sauce mix with all the yucky bits thrown in, ever again!