Many people who have an outdoor misadventure quickly point out that having and using the 10 essentials allowed them to survive!
Flashlight and spare batteries
Many people take just a little too long on a hike and are caught by darkness, and it can get really dark under the trees. We've found people who only got lost after dark and could not stay on the trail. Some of these people even hurt themselves after falling once they left the trail!
Extra Food and Water
If you're delayed by weather, a little food and water can make an uncomfortable situate much better. You're less likely to panic, and it allows you to think clearer so you don't turn a little mistake into a big one.
Extra clothing (rain, wind, water protection)
If you're delayed and out at night you know how cold it can get. Even a jacket and a hat can help keep much warmer.
this useful item can make tent pegs, whittle wood for a fire, cut rope and hundreds of other things that can help you survive.
Navigational Aids (map, compass, altimeter, GPS, chart, radio, mobile phone) and know how to use them
Without (at the very least) a map, and a compass and the knowledge of how to use them, you're really at the mercy of whoever built the trail you are on.
A candle helps provide warmth, but also lets you start a fire and gives you light
First Aid Kit and know how to use it
small accidents are a big problem if you have nothing to treat them with
Large Orange Garbage Bag
When we tell people to bring one of these they think we are crazy, but every SAR member has them. They're VERY useful as an emergency shelter, and they can also be used as a signaling device for helicopters
Fire Starter: matches in a waterproof container or a full lighter
Sun Protection (Glasses, Sunscreen, Hat)
the sun is a force to be reckoned with. Without sun protection, burns and sun stroke are almost certain on a sunny day
Wikipedia has an excellent article on the Ten essentials.
The basic idea here is to be prepared for bad luck or misadventure by having the minimum necessary to survive until help arrives. Most accidents in the backcountry, and most searches done by our teams could have been avoided had the subject carried even some of these items.