Canon BP-511A Lithium-Ion (Li-Ion) 1100 mAh

BP-511's are lithium-ion batteries, and as such can be recharged safely at any charge state without significantly reducing the effective life.
Some batteries (like those in the 1D) must be periodically discharged completely to maintain battery life. This is not necessary for the BP-511.
The storage capacity of lithium-ion battery packs decreases gradually with use. Typically, the BP-511 can handle about 300-400 full discharge/recharge cycles without a noticeable loss of capacity. After that, performance, as measured in the number of shots per charge, decreases quickly and the battery pack becomes unusable.
The battery level displays in EOS DSLRs that use BP-511's change their readouts in 4 steps (full, half empty, blinking, nothing) based on specific voltage levels, which explains why limited shooting can produce a dramatic change in read-out.
Lithium-ion battery packs, like most other secondary (i.e., rechargeable) batteries, very typically "recover" to a slightly higher voltage level when allowed to rest for a short period after use. This characteristic is different from primary (non-rechargeable) batteries like standard AA alkaline cells - again explaining why the meter reading may change for the same battery after it's been sat in a warm pocket for a while.
When two BP-511 battery packs are installed in the BG-ED3, the camera draws from the pack with the higher voltage level first until it equals the level of the other battery pack, then both packs are drained simultaneously.
In a recent post, Chuck has confirmed that there is no difference in battery drain whether the camera is off or on provided neither of the LCDs is active. Once the metering display has turned itself off after the requisite six seconds, you can just rely on the shutter button to wake the 10D up rather than turn the camera off and be forced to endure the several seconds' boot-up procedure.