This attribute of a warrior found on the overview determines how long a warrior can keep up their offense, defense, or just keep standing. All styles use the same physical stats and the computer determines their endurance the same way, using those stats as a base. But the actual endurance of a warrior can vary up or down from that base depending on luck (good or bad). Like skills, each warrior can be gifted, mode, or hosed in their starting endurance, and that giftedness or penalty seems to stick with them permanently. Possible endurance levels, from lowest to highest are: very little, poor, normal (no comment), good, great, tremendous, awesome.
Endurance can also be raised, in order of importance, with WL, ST and CN trains. After training endurance to a warrior's first new level, I find it usually takes about 6 total trains, on average, to get to the next level of endurance. If a warrior is gifted, as training continues, that higher level of endurance appears to stick with them. It would be difficult to list numerous data points here to give you a better feel for what endurance to expect in your new warrior, but if you want more data, try this web site and look at the chart:
http://www.bit-net.com/~johnh/calc.cgi?end
ENDURANCE BURN
How fast endurance is used depends on the style of a warrior, their activity level, their offensive effort, and armor/weapons carried.
1) Burn rate by style -- This is tricky to tell as nobody runs all styles with the same strategy and armor regularly. But here is an approximate rate of burn by style from highest to lowest, in my humble opinion:
LU - WS - SL - BA - PL - ST - PR - AB - PS - TP
Personally, I find the last five extremely difficult to separate, but usually the more active styles burn faster due to faster strategies and more offensive skills, so I tried to put them in order of the most active, typically. There are numerous exceptions of course.
2) Activity Level -- Warriors running at higher levels of activity burn endurance faster no matter their style, period. It may be that running on a warrior's favorite rhythms allows said warrior to continue at that level longer than otherwise. When a warrior gets tired, a strategy with a higher activity level will inhibit them from recovering their endurance as they will try to keep moving.
3) Offensive Effort -- The more a warrior swings, the more tired they get. Of course, if your OE is high, but the other guy is doing all the swinging because they have the initiative, you aren't burning as much endurance. Endurance recovery is also inhibited if offensive effort is kept up when a warrior is tired.
4) Weapons/Armor Carried -- The more one carries, the faster a warrior gets tired carrying it. Easy.
EXHAUSTION
Warriors who are exhausted or tired will see lines in the fight reading, 'no longer has the endurance to put up much of a defense', or 'staggers with exhaustion'. You will see the former line if your warrior is exhausted and is attacked. Such warriors are easier to hit and have a difficult time using their defense and parry, which are penalized or even non-existent while they rest and try to recover their endurance.
ENDURANCE RECOVERY
Over the course of a fight, warriors who become tired will often 'fade back, snatching a much needed moment of rest' or some other similar action. This is basically a breather for the warrior to try and recover some endurance so they can keep fighting. Kind of like a climber pausing briefly to catch his breath and recoup. If the warrior is not defeated while recovering, they will continue eventually, or try to. For high burn styles, the very thought of continuing often makes them fade back again and they may stand around for a while if not hacked down. They may also leap about continuously, holding onto the initiative, but lack the endurance to actually swing! Very low activity and offensive effort allows easier recovery than even moderate strategies by telling your warrior to effectively give up the initiative and chill. Of course, you run the risk of getting attacked while standing there. Low burn styles can actually, if running slow enough (i.e., never attacking!), stand around and recover their endurance almost as fast as they lose it, making REALLY long fights possible between two such warriors.
WILL CHECKS
Lastly, related to endurance, are "Will Checks". When a warrior is exhausted, this check is performed by the program to decide if the warrior wants to go on for just a bit longer, to hang in there. It occurs often in longer fights, especially with the Total Parry style, which often wins by exhausting their opponents. A failed will check results in the warrior collapsing from exhaustion. A successful check allows an exhausted warrior to continue and try to recover more endurance. Additionally, will checks determine whether a warrior surrenders, usually due to being wounded. A will check is determined by just that, WILL. If your warrior has a low will, they will surrender or collapse more often than those with a high will.
Lastly, kill desire affects will checks. A low kill desire will make it more likely that a warrior will fail his will check and surrender, therefore live. A higher kill desire makes the warrior more willing to gut it out and fight to the end, helping his will checks succeed. This may cause warriors to get killed more easily, unless they win. This kind of death is due to a warrior who refuses to surrender, giving their opponent more chances to try and kill them, or due to increased trauma from more hits to a specific body location that can result in an infirmary death.