Tournaments, mock battles, first appeared at the end of the eleventh century/beginning of the twelfth. Because by that time it was fairly well understood (at least in the abstract) that Christians should not kill Christians (as discussed in a previous post), the knights who had been trained their whole lives as warriors wanted a chance to demonstrate their skill. Church leaders would have preferred them to go off on Crusade, but the knights did not necessarily want to go off on a long and dangerous trip, where they would likely come home broke if they came home at all.
Of course, one could be killed in a tournament, even though that was not the purpose. The swords did not have edges, but they still made fine blunt instruments. And falling from a galloping horse is an excellent way to break one's neck. Because the church believed that a tournament brought out all of the worst vices--pride and anger as well as potentially manslaughter--whole tournaments might be put under excommunication. Someone killed in a tournament was not supposed to be buried in the churchyard but rather at the crossroads with a stake through his heart, the same as a suicide.
Twelfth-century knights were not deterred nor inspired to go on Crusade instead. If one went on Crusade, one was either trying to find salvation or else to join in the general excitement when a duke announced he was off to Jerusalem.
It was possible for an excellent tournament fighter to make his living on the circuit. William Marshall, who was companion to one of the sons of Henry II of England and later regent of England after the death of King John, got his start fighting in tournaments. Losers forfeited their horse and armor to the winner, who generally allowed the loser to buy them back.
Although the modern view of tournaments is two knights with long lances galloping at each other in a ritualistic way, in practice twelfth-century tournaments could be a lot more chaotic. As well as jousts, the face-offs between two knights, there was the mêlée, a free-for-all that could take off cross-country and go on all day. At one point the knights from Flanders were late for a tournament and announced that they would just sit and watch. However, as the mêlée was winding down, and all the other knights were exhausted, the Flemish knights donned their armor, mounted up, and quickly captured everyone in sight. This was universally agreed to be a fine trick.
At many big tournaments, there would be a sort of pre-tournament the night before, to weed out the weaker fighters. This "bohort" was typically fought in regular clothes, not armor, and involved poking more than striking. It was a sign of ostentatious wealth to wear very fine clothing to the bohort and have them ripped to shreds.
Women did not participate directly in tournaments. But they certainly were spectators, cheering on their favorites, often determining who was the winner, the one who had fought the best. The knights of course wanted to impress the ladies (adding lust to the list of vices a tournament could excite).
With the invention of gunpowder, the fighting skills honed in tournaments no longer played much of a role in real battles. Nonetheless, tournaments continued to be popular. They could become extremely elaborate, requiring knights to prove noble ancestry several generations back in order to take part. As armor became heavier and heavier and the warhorses thus larger, the knights had to be winched up into the saddle and strapped in place. The late medieval church decided there was no problem with tournaments, even though people were still killed in them--including the heir to the French throne in the sixteenth century.