first time equipping titan armor

What you're seeing is flamethrowers in the floor firing on the soldier, and it is indeed a demonstration of the armor's immunity to fire.

What that means in the game is that areas on fire, which would normally count as walls and force your soldiers to go around, soldiers wearing titan armor can pass right through as if the fire wasn't there. Titan armor also allows them to run through the gas clouds created when thin men die without being poisoned, and will not be affected if a thin man spits poison on them (exactly like when a soldier is carrying a medikit, which kind of makes a support wearing titan armor a little redundant).

On a side note, you'll see a similar video when a soldier first equips the archangel (flight), ghost (cloak), and psi armors (what I call a psi pulse). You also would have seen a video if you equipped a soldier with skeleton armor (firing the grapple and lifting off the top of the screen, then dropping back down).
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There are 10 types of people in the world. Those that know binary, and those that don't.
GT:Talon Omega. If you send an FR please tell me where you got my GT.

That's weird. I've always gotten skeleton armor shortly after getting carapace, and long before titan was available. I don't remember what research unlocks skeleton armor.

You're not missing too much without skeleton armor, though. It provides a 3 point HP boost (lowest of all armors), a 10 point defense boost (this can be useful, as it slightly improves the effect of cover), and a grapple that allows soldiers to reach rooftops or other high areas without having to find stairs, ladders, or a drainpipe.

Also, carapace doesn't have a video, as it doesn't have a special function. All it provides is the 4 point HP boost, and nothing else.
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There are 10 types of people in the world. Those that know binary, and those that don't.
GT:Talon Omega. If you send an FR please tell me where you got my GT.