You can think of a battery as a chemical repository for electrons. It will have two characteristics that are typically measured: output voltage ("volts") and current rating ("amp hours").
The output voltage of the battery is calculated by multiplying the potential voltage of a cell by the number of cells (when connected in series). A cell has a fixed potential voltage, which is a chemical property determined by the materials that electrons travel from and to through the electrolyte. To chemists, this is the "redox" potential. You can't change it.
A car or motorcycle lead-acid battery has six cells in it, connected in series, giving us a total potential difference of 12V. You can think of "potential difference" as the "potential energy" that an electron can use up to get from its high energy state (on an anode) to its low energy state (on a cathode) -- and to make that traversal, it has to go through a conductor (your bike's electrical system), and some metal has to dissolve into the electrolyte solution. [FWIW recharging puts the metal back where it was, and "loads up" the electrons on the anode again.]
The AH (Amp-Hour) rating of a battery tells you how much current (how many amps) it can deliver, and how long it can sustain that rate of delivery -- i.e. how many electrons, and at what rate is the battery able to deliver.
One ampere is measured when 6.02 x 1023 electrons (one mole of electrons) pass a given point in a conductor in 1 second.
Remember, electrons will not leave their stable states until they "know" they can get to a place where they have less energy, and they also "know" how many of them go at once, by the resistance of the conductor (bike) connecting the cathode to the anode. In fact, I=R/V gives you the current (I) that will flow, given a particular resistance (motorcycle or car) for a given potential difference (V).
As you can see, V is fixed due to the fact that we are using a lead-acid battery composed of six cells. R is fixed due to the fact that bike's electrical characteristics don't change depending on the battery available. So, if you try to use the car battery, fewer electrons will flow out of it because the resistance of the electrical system in the bike is higher than in the car.
Think of it like this:
Imagine the battery as a great source of drops of water: Say, a big water reservoir.
There is a pipe of fixed diameter coming out of the reservoir, leading to a lake below. Think of this pipe as your bike's electrical system.
Now, at the top of the reservoir there is water with lots of potential energy (it wants to fall to the lake) -- BUT the speed that the water can fall is governed by gravity, and no matter how much water flows, each individual drop (electron) falls through the pipe at a fixed speed (voltage).
How MUCH water flows is entirely dependent on the width of the pipe attached to the reservoir. The bigger the pipe, the lower the resistance, and the more water can get through.
(To finish the battery analogy, the top of the reservoir is the negative terminal of the battery, and the lake at the bottom is the positive -- that's the direction electrons flow)
Got it now?