Bad luck and a failed saving throw, perhaps. A poor decision that just didn't work out the way you hoped. The inability to run away fast enough, or some other misfortune occurs, and the character's hit points reach zero, then the referee's words, "you're dead!" rings out across the game table. Not to worry, death in D&D isn't necessarily final. It may just mean you need to get your character resurrected, or perhaps now is the time to roll-up a new character? One who will likely be even more interesting to play than the recently deceased - for every new character is full of possibilities!
We role-players can put a lot of effort into our in-game avatar. We get attached to our player character, either through putting a lot of effort into character generation or through the events which happen during play resulting in emotional attachment. Loss of a favorite character can result in loss of desire to play the game. All that time, all those experience points, gone and wasted...
Let's suppose that the dead character had advanced in levels, yet resurrection/raise dead is not an option. You have played this character in company with the characters of several of your friends for months and all the PCs have all advanced in levels to the point that playing a 1st level character among higher levels may seem like less than fun. This may appear like a problem. How will a new 1st level character fit in with the higher level party? How can they contribute? Fortunately, the creators of the world's first fantasy role-playing game gave us a solution.
Looking at the numbers, we can see that higher level characters advance at a slower rate than lower level characters across all the classes. Some classes advance much more quickly than others (that's part of "balance" in the old school game). Looking at the OD&D fighting man class, we see that it takes 8000 experience to reach Hero (4th level), but it takes an additional 8000 to reach the next level, Swashbuckler (level 5). In the time it takes our hero to advance from level 4 to level 5, a fresh recruit can advance through the first three levels and be entering level 4 - one level lower than the chap who didn't die. The first five to seven levels are all set up this way so that the next level requires twice the experience points. Magic Users advance slowest, Clerics have the quickest (lowest exp totals) advancement. Take a starting level Cleric and by the time the party's Magic User advances from 4th to 5th level 9 (10,000 - 20,000), your newly christened Cleric will be just 2000 exp short of 5th level (Curate - 12,000).
Sure it may require hanging back and sheltering behind the front line fighting men for a few sessions, but that is a good way to get to know the magic user who will be back there with you. As a Cleric, even one of lower level everyone will appreciate your turn undead ability and cure light wounds spell (once you reach level 2 and can cast, that is). Choose a fighting man and shoot arrows for your first few sessions or fight from the second rank using a spear. Even a first level magic user gets Charm Person or Sleep, both are useful spells. It seems Gary thought this one through and provided a solution for helping a starting character catch-up to the higher level PCs within about a level so that players who lose a character won't feel that they are too far behind for long. Thank you, Gary!
(...and yes, the bearded figure pictured above, taken from Vol. 1, is labeled as a "Goblin"!)