The 3 important things to consider when looking at a battery:
Voltage:
The voltage of a battery is proportional to the top speed your ebike can go. If you have 2 identical ebikes, one with a 36v battery and one with a 48v battery, the one with the 48v battery will have a 33% higher top speed.
Amp-Hours:
The amp-hours of a battery literally represents the ‘amps it can deliver for an hour’. This means a 15AH battery, fully charged, can deliver 15 amps constantly for 1 hour. This can be broken up into any timeframe, meaning you can get 7.5 amps for 2 hours, 5 amps for 3 hours, etc. It is the amount of ENERGY stored in the battery.
Discharge Rate:
Not all batteries are capable of powering all ebikes. Generally speaking, the max discharge rate of a battery is 3x its capacity, or 3x its Amp-hours. If you have a 15AH battery, you can expect to be able to pull 45 amps MAX.
A high AH and high discharge rate is a good indicator that a battery uses quality cells. NEVER trust the battery specs listed by ebay, amazon, or craigslist sellers. The battery is the most important part of an ebike so don’t cheap out on it!