What to do with excess fat in meat?
What you describe is known as 'rendering' the fat -- you cook it until the liquid comes off.  But the goal isn't to eat the fat, but to create something oily that you can cook with.

If I'm just rendering for later, I'll strain the fat before putting it into a container to keep in my fridge.  If I'm going to be immediately cooking with it, I'll chop it up first (it helps to put it in the freezer for 10 to 30 minutes so it'll firm up before cutting).  Chopping it up also gives it more surface area so it renders faster.

But it's important to note -- there are a few things that get trimmed from meat besides fat:


tendons : ribbons, usually bright white; used to connect muscles to bones.  They need to be removed, as they're always tough and chewy.
silverskin : slightly greyish shiny film; Also needs to be removed, as it's like chewing rubber when cooked.


If either of those two are in there, you'll want to discard the fat bits after they've been rendered.

In other situations, you can cook the fat bits until they're browned, remove them with a slotted spoon, and let drain on a paper towel.  You'll end up with crunchy bits that you can add back into the dish later (like the fatty part of bacon)

...

Some other uses (besides feeding to birds) :


Throw it in when making a pork stock.  The fat will help to cap the stock when you store it in the fridge.
Save it to grind up when making sausage.  (if you make sausage)