Battery terminal voltage as it relates to its proper functioning
It is very easy to do a quick check of battery voltage with a voltmeter. If your 12v battery measures less than 12v, chances are good that it has a problem, especially if it is not supplying current to a load. But if it does measure 12v, it may still be in a discharged state, and unable to supply much current - when asked to do so, output voltage drops to a much lower value.
The testing voltmeter is designed to load the battery very lightly - a proper test of a battery (or any other voltage source) is called a load test where the battery is asked to supply significant current, while its voltage is monitored. A good 12v battery under test will sag to a lower voltage under load, but falls only by a small amount.
testing car battery
Note that a battery may be good, but electrical connections to it are oxidized, or dirty. Re-seating, cleaning these connections can help reduce voltage sag.
We have a simple electrical model for voltage sources, including batteries. It is not entirely accurate for chemical cells, but gives roughly the sagging characteristics mentioned:







simulate this circuit &ndash; Schematic created using CircuitLab
This is a good, charged battery. If you were to short the +ve terminal to the -ve terminal with a short circuit (don't try this), 200 amps would flow through that short circuit, generate a lot of heat, and would discharge the battery in short order.
A discharged battery still has nearly 12.6 volts at BAT1, but R1 has increased significantly. If it rises to 600 milliohms, you'd still measure 12.6 volts with a voltmeter. But the short-circuit test would only supply 20 amps. For car starter motors, the current flowing from one terminal to the other is what provides the cranking force. Current is more difficult to measure than voltage.