There's a limited time game mode called Snow Battle ARURF where all players get massively reduced cooldowns. I'm assuming that's what you're referring to. Just click the Play button on your client and it'll be the right-most option.
A player can acchive reduced cooldown by these ways:
1) Items that give % CD reduce
2) Runes
3) Ability of the champion himself
4) Game mode such as URF
For Twitch:
1) Here is CDR item list and every information about Cooldown in the game
2) Runes that gives CDR:
a) from the Sorcery path: The Ultimate Hat (just for the ult 5%-15%),Transcendence (10% since 10 min)
b) from the inspiration path: Cosmic Insight rune Cosmic Insight (5% and incread cap from 40% to 45%)
3) Twitch's Ambush (Q) cooldown is refreshed if an enemy dies while affected by Deadly Venom (passive). more information here
1) Items that give % CD reduce
2) Runes
3) Ability of the champion himself
4) Game mode such as URF
For Twitch:
1) Here is CDR item list and every information about Cooldown in the game
2) Runes that gives CDR:
a) from the Sorcery path: The Ultimate Hat (just for the ult 5%-15%),Transcendence (10% since 10 min)
b) from the inspiration path: Cosmic Insight rune Cosmic Insight (5% and incread cap from 40% to 45%)
3) Twitch's Ambush (Q) cooldown is refreshed if an enemy dies while affected by Deadly Venom (passive). more information here