Split second is a static ability that essentially makes a spell uncounterable. It works by not allowing any players to put any spell or activated ability on the stack as long as the spell with Split second is on the stack. Split second was introduced in Time Spiral. 
A historical note is that, in a way, Split second harkens back to Interrupts, which also couldn't be responded to with instants or activated abilities, only other interrupts.
- Players still get priority while a card with split second is on the stack.
- Split second doesn't prevent players from playing mana abilities.
- Split second doesn't prevent triggered abilities from triggering. If one does, its controller puts it on the stack and, if applicable, chooses targets for it. Those abilities will resolve as normal.
- Split second doesn't prevent players from performing special actions. Most notably, players may turn face-down creatures face up while a spell with split second is on the stack. For example, if Sudden Death is targetting a creature you control, you may flip up a Willbender to change the target of Sudden Death to another creature.
- Split second won't affect spells and abilities that are already on the stack.
- If the resolution of a triggered ability involves casting a spell, that part of the effect won't work if a spell with split second is on the stack.