What is to caramelize and how can this enhance a food's taste?

Yes, I think you're on the right lines. "Caramelising" comes shortly before "burning" and involves sugars. These sugars are either contained in the ingredient naturally, or can be added.

For example, you can caramelise the natural sugars on the exterior of a piece of meat, like a steak. This brings the delicious savoury meaty taste out. It's an important step when making bolognese sauce/ragù, for example.

You "brown" the meat in a little oil in a pan over a highish heat. If you crowd the pan with too much minced meat, or stir too much, you'll create steam which will make the meat turn grey instead. You lose out on the meaty taste and your finished dish is rather lifeless.

As you mentioned, it also works with fruit and vegetables, although in the case of fruit, you would probably add a little extra sugar, such as in a flambée. You might also add a little sugar to onions to make a deep-brown French onion soup or onion marmelade. As you suggest, all this is to add flavour to the dish.

Perhaps you're thinking of a typical beef stew where you might dip the meat pieces in seasoned flour before browning them, then adding liquid and simmering for a few hours. Meat sauces would benefit from this browning, too. Soups without meat, perhaps less so.

Just sweating the vegetables in butter/oil before adding the liquid brings their flavour out. And you can caramelise sugar by heating some dry in a pan until it turns to "caramel". You can use this to make fancy spun sugar decorations or a topping for popcorn, amongst other things.

Make sure you don't get it stuck to your fingers/lips/tongue as it's veeery hot and hard to wipe off! Yes, I think you're on the right lines. "Caramelising" comes shortly before "burning" and involves sugars.

These sugars are either contained in the ingredient naturally, or can be added. For example, you can caramelise the natural sugars on the exterior of a piece of meat, like a steak. This brings the delicious savoury meaty taste out.

It's an important step when making bolognese sauce/ragù, for example. You "brown" the meat in a little oil in a pan over a highish heat. If you crowd the pan with too much minced meat, or stir too much, you'll create steam which will make the meat turn grey instead.

You lose out on the meaty taste and your finished dish is rather lifeless. As you mentioned, it also works with fruit and vegetables, although in the case of fruit, you would probably add a little extra sugar, such as in a flambée. You might also add a little sugar to onions to make a deep-brown French onion soup or onion marmelade.

As you suggest, all this is to add flavour to the dish. Perhaps you're thinking of a typical beef stew where you might dip the meat pieces in seasoned flour before browning them, then adding liquid and simmering for a few hours. Meat sauces would benefit from this browning, too.

Soups without meat, perhaps less so. Just sweating the vegetables in butter/oil before adding the liquid brings their flavour out. And you can caramelise sugar by heating some dry in a pan until it turns to "caramel".

You can use this to make fancy spun sugar decorations or a topping for popcorn, amongst other things. Make sure you don't get it stuck to your fingers/lips/tongue as it's veeery hot and hard to wipe off!