Ultiduo is a competitive format consisting of two players on each team, a Soldier and a Medic.
This gamemode is played on small KOTH maps that are specifically made for it. Ultiduo is often played by the 6v6 combo, containing the Medic and Pocket Soldier, to build up synergy between each other.
ETF2L has a whitelist for Ultiduo allowing the default loadout for both Medic and Soldier with few unlocks for both.
Naturally reskins of stock weapons (e.g. strange weapons, festive weapons, botkiller weapons, the Frying Pan, Conscientious Objector, ...) are allowed.
The Disciplinary Action
The Crusader's Crossbow
Ultiduo cups are often held by leagues or sponsored by community members. As each team requires only 2 players these cups are usually easy to set-up, making it a viable option for offseason cups.
It is generally very welcomed by top players as it is a very good source of practice and it is also widely considered to be a fun gamemode.
Ultiduo hails from a similar competition from TF2's predecessor, Team Fortress Classic, called Ultimate Soldier (also made by ozfortress). This pitted two soldiers against each other in a 1v1. Shotgun was often more powerful back in these days, as the spread of it was much smaller, allowing you to 'snipe' your enemy. This was often frowned upon, but typically the only way some players with poorer internet connections could compete.
The original ultiduo maps were not koth, and victories were awarded based on who scored the most frags. The gameplay has evolved over the years, especially with unlocks and the increase in player skill.