The video is here, by Kuya.
In Japan, it's been a long-time rumour that the Arenas in FE7 and 8 have a "Serious Mode" that can be activated, changing the Arena organizer's dialogue (important distinction) and upping the challenge. Simply winning continuously doesn't activate it, and as there was no obvious way to make anything change, it was often dismissed as internet BS.
Well, this guy spent five whole years researching this, and finally managed to discover how to activate it. Of note, the author says he checked with someone overseas and found that this wasn't in the English versions of FE7/8.
To activate it, you have to win four Arena matches in a row, then on the fifth fight onwards, soft reset any time between your unit landing the killing blow (confirmed victory) and getting paid. If the trick is successful, you'll be taken back to your unit landing the killing blow on the enemy, except you'll notice that the enemy's HP should've changed, as well as your damage, hit rates, etc. That's how you know Serious Mode has been activated.
Once it's been activated, the Arena handler's dialogue changes when you send the same unit to the Arena again. He says:
This is the Arena. Oh, it's you again.
You've made me lose a lot of money...
If you're gonna keep going, then I have an idea.
I'll prepare some worthy foes.
Once Serious Mode is activated for a unit, it's permanently active on that map, even if you concede, which is how it's different from the regular Arena grinding power ups. It's possible to triggger Serious Mode on multiple units per map, but using the author's method, further units may take more than 5 wins to trigger it, so you have to keep performing the trick on wins until it works.
The enemies themselves aren't particularly stronger than just winning Arena consecutively normally, though it does up the baseline strength of the enemies even if you lose your streak. On Sacred Stones Hard, which has harder Arena enemies than FE7, the author's Joshua fought a Wyvern Lord with 98 HP/27 Str/29 Skl/27 Spd/0 Lck/11 Def, which as far as I know is possible to encounter with just regular grinding.
If you're attempting this trick on your own, note that the stat shifting when triggering Serious Mode can actually cause the outcome of the fight to change because of the differing hit rates etc.
Based on the fact that this feature isn't in the overseas versions when localized FE7 had made changes such as restoring Lyn's Sol Katti animations, the author thinks this is simply unused content that can be accessed through unconventional means, and not a bugged feature. Since FE8 reused a lot of things from FE7, it probably got ported into that as well.