What the display shows is the minimum of
1) battery capacity, based on measurement of used power, or
2) time to battery exhaustion based on recent heavy usage
Lithium ion battery capacity changes depending on how quickly the battery is being discharged. For example, on the graph from battery university, a high rate of discharged (2.0C) results in the battery hitting the lowest usable voltage at 2300 mAh. But if the battery is drained at half that rate (1.0C), then the battery capacity is 2900 mAh. So, if you've used 1250 mAh, the available power is either (2300 -1250)/2300=50%, or (2900-1250)/2900=57%, depending on the rate of power draw. And if you have a low power draw, or if you take long breaks during big climbs, capacity could be 3300 mAh or 62%.
BU meta description needed...
batteryuniversity.com
You can visualize this as like 20% of the battery charge being available immediately to a motor. but the the other 80% of the battery power has to drip through a small tube before it can be used. Technically speaking, the first 20% are free electrons on the surface of the battery, and the last 80% require a slow chemical reaction to take place, which takes about three hours until it completes and all power is available. Though not entirely accurate, you can very roughly estimate that charging time of 2.5-3 hours means that the discharge rate is also 2.5-3 hours.
So, if you go up a steep hill that draws a lot of current, the battery gauge correctly indicates that if you keep going at this rate, your battery is going to be exhausted before it is fully drained, and represents that as a lower battery percentage.
What I've noticed on my Propella Pro is that after going up a long, steep hill (San Francisco), the battery will show this lower percentage for like 5-10 minutes of assist over level ground. The software will show the lower of the two values, but capacity % never rises, which is probably the less confusing of their software choices.