Lithium-Ion batteries have a limited number of charge-discharge cycles that they'll withstand untill they don't hold a sufficient amount of charge. these days, for a cheap battery, you can only guarantee 100 charge/discharge cycles before it gets to about 50% or 60% charge capacity.
additionally, discharging lithium batteries fully will wear them out faster than not. there is only ONE good reason to discharge a laptop-battery all the way deliberately, which i'll get to in a second, otherwise, you should try to avoid it.
incidentally, Lithium-ion batteries only last a few years whether you use them or not. they used to only last one or two years, these days it's more like 3 or 4 if they're good quality.
now, Laptop batteries have sophisticated control circuits which monitor their charge status, temperature and all sorts of other things. these circuits make note of when the battery loses capacity, and report the batteries ACTUAL remaining capacity to the computer.
when the total capacity changes and the circuitry doesn't detect it, then it's record of the batteries capacity will be wrong, this can lead to your computer giving you low-battery warnings when it's not on low battery, or thinking it's got more battery than it has, and your computer will just shut down unexpectedly. thus, it's reasonably sensible to fully charge your laptop, and then discharge it fully about once a month.
now, some laptops have battery care hardware or software, which ensures that the battery isn't charged when it's full. laptops that don't will continue charging the battery when it's full, which will kill the batteries VERY fast - if your laptop doesn't have care hardware/software, remove your battery if you're going to be using AC for more than 4 hours or so.
additionally, heat kills lithium batteries very fast. if they exceed 40 degrees (Celsius!) when in use, they'll lose capacity exceedingly fast.
similarly, if they're left in high-heat for extended periods of time (about 45 to 50 degrees for an hour or more) then they'll also die.
if you're going to remove a battery and leave it in storage for an extended period of time, then leaving it between 40% and 70% charge will be best for its lifespan. additionally, putting it in a sealed bag and then putting it in low temperatures (but never below 0 deg Celsius) will prolong it's lifespan.
lastly, never place a lithium battery in a fire (it'll explode) or pierce it with something metal (it'll also explode).