Question: When a garage hooks up their battery tester what does it actually measure and how does this differ from tests you might perform yourself with a volt-meter?

For example, recently a garage measured my battery and said it was bad because it scored "around 40" when it should have been "around 80". I have no idea what these numbers mean, CCA (cold cranking amps) perhaps?

Answer: 
There are two things that professional battery testers can measure. One is to somehow based on the voltage measure the charge level. Another is to measure cranking amperes.

Of these, the second measurement (cranking amperes) is accurate. Unfortunately, old batteries don't die by having reduced cranking amperes: they die by having reduced capacity. So, the cranking amperes test for a battery that has 95% of its life behind and 5% of its life left will still show that the battery is good.

The first measurement (charge level deduction based on voltage) is very hard to do. At the minimum, you need temperature compensation because temperature has an effect on open circuit voltage. Furthermore, measuring the temperature of the measurement equipment is not enough, the temperature should be measured on the battery. Also, you should leave the battery rest for long enough and garages on busy schedule don't have time for that. Even when all conditions are perfect, the voltage between full battery and a nearly empty battery is only very slightly different.

40 and 80 are way too low to be cranking amperes. I suspect the measurement equipment deduced that your battery is 40% full and it should have been 80% full. But remember that these percentages are very hard to be calculated correctly.

Because it's practically impossible by measurements to identify a battery that is dying, I recommend you to change the battery if it's too old. For example, if you plan to keep your car for 20 years, you could change the battery twice in its lifetime: once when it's about 7 years old and the second time when it's about 14 years old.

I let a garage measure my battery using such an equipment because they offered the service for free. Their diagnosis was: the battery is fine (cranking amps good) but requires a recharge (the charge percentage wasn't close to 100%), and recommended me to occasionally drive for long durations. Well, I had occasionally driven the car for long durations. I had also noticed that when the start/stop system operates to start the engine, the headlights flicker. The battery was 5 years old. It never failed to crank the car even at -20 degrees Celsius temperature, but I suspect it was nearing the end of its lifetime.

The ultimate test for battery would be to test its ampere-hours. However, that requires a deep discharge which lead-acid batteries don't like. It also causes you to lose radio settings. The measurement would take many hours, something for which garages don't have time.

If you know the current draw from your headlights, you could leave the car with the headlights on and see for how many hours they are still on. For example, if the headlights are 120W = 10A @ 12V, it means that a 50 Ah battery should be able to keep the headlights on for 5 hours. This will however, as I said, lose your radio settings.
A voltmeter can tell you part of the story.

The second part is twofold. One is how much your battery can deliver in the cold. Cold cranking amps means worse case senerio.
Two is how long that battery can deliver some amount of current over time.
Usually both figures are published on the battery or someplace. One tends to be more important over the other based on it's use.

Now as to what a tester can do. One is simple resistance load over maybe 10 seconds. This was the standard used for maybe 100 years. Now there are a few "electronic" testers that send a signal into the battery for some result. Both may read differently but can provide some clue as to quality.