Cooking vegetables down is a common cooking  practice in the Louisiana kitchen. You don't do this with every dish, only for the ones you want to have a special vegetable consistency and color. Examples are gumbo, stew, jambalaya, roasts, etc. 

What I've done here is put together some pictures of the process along with explanations of each step. I did this batch for a pot roast. I seared the pot roast, removed it from the pot and continued to cook it in another pot. 

Step 1

2 onions chopped

On a medium fire with a little oil in the pot I added the onions.

I let them slightly wilt and turned the fire up just a little so most of the onions would turn brown.

One the onions got the browned stage I wanted I added the bell pepper and celery. I also added about 1/8 of a cup of water; just enough to almost cover the bottom of the pot, and, turned the fire down to just below medium.

Here's where you have to watch things a little more closely. You should keep a little water in the pot at all times stirring every five minutes or so. Notice below the brown liquid. That is the result of both browning the onions and searing the roast. 

Below, the trinity has cooked a little more. This is probably 45 minutes into the process.

And finally here is the result 90 minutes later. Notice that it's about 1/2 the original size.

From here on you would throw in the roast, or add browned chicken or whatever and continue to cook as you normally would.