In survival, there are two different Rule of Threes talked about. This article will be a quick summary of what they are.
Rule of Threes as it applies to Survival Equipment/Gear
This rule of threes is all about redundancy. The idea is to have at least three ways of obtaining every survival essential. Fire is one such essential, so for instance you could have a lighter, some matches, and a ferrocerium rod.
For water, that might be chlorine tablets, a water filter, and a pot to boil in.
For cutting tasks, that might be a knife, a multitool with a blade, and a small backup neck knife.
To make this rule work even better, it’s good to have at least one of the items in each category attached or strapped onto your body, in case you are separated from your pack in an actual survival situation. An example scenario might be: you went on a white water rafting trip, fell out of your raft, and washed up ashore without your backpack, which continued flowing downriver.
Rule of Threes as it applies to Time Left to Survive
The other rule of threes talks about how much time you can survive for without something. The general rule is:
3 weeks without food. (Assuming you stay put and engage in minimal exertion.)
3 days without water. (Above applies.)
3 hours without shelter. (Overnight survival can be tricky due to exposure to elements and hypothermia.)
3 minutes without air. (Bring your gas mask?)
One absolutely vital essential omitted out of the four above is first aid, but this is because it’s impossible to quantify any kind of general survival time for this. You could die in 2 minutes from major arterial or venal bleeding, or after weeks from an untreated infection from a cut.
I’ve seen people refer to both of the above rule of threes, seemingly without any awareness or at least mention of the other one, so I thought it would be useful to distinguish between both of them on the same page. I hope this helps!