The Set-Up your guy is talking about usually involves three points:
- Adjusting the truss rod - neck relief
- Adjusting the action
- Adjusting the intonation
The truss rod is a metal bar of some sort, embedded into the neck of your guitar. It is used to adjust the curvature of the neck. All guitar necks have a certain degree of curvature - convexity or concavity - this is necessary for the strings to be aligned properly relative to the neck, when playing at various points on the neck. The truss rod is used to bend the neck slightly - stretch it to make it more convex, or contract it to make it more concave. It's called neck relief, and depending on your strings, your action,the environment and you personal preferences, the degree of neck relief needed can change. Often when changing strings, a tweak is needed.
The action refers to the height of the strings above the fretboard - higher action or lower action with reference to the fretboard. Some players prefer higher action, others lower. Some guitars sound better with higher or lower action and some strings work better with higher or lower action.
There are various ways of adjusting the action. For example, screws on the bridge, bridges that raise and lower the height of the strings or can be moved to change the action.
On acoustic guitars there are usually fewer options available for making adjustments. I don't know too much about the details of setting up an acoustic. The bullet points will be pretty much the same, but how to do them will differ - among electrics they also differ. @Tim in the comments says that the saddle itself may need trimming in some cases to lower the action on an acoustic.
Adjusting the action of the strings works in conjunction with adjusting the truss rod. For anything more than very small changes they should be done together.
Intonation refers mainly to each string being in tune with itself. On a guitar for example, the twelfth fret should be exactly one octave higher in pitch than the open string. Various factors can effect the intonation and there are various ways of adjusting it, similar to the action.
Changing strings can require adjustment of all three factors - particularly action and neck relief. These adjustments are tricky and one can impact the other, so it requires expertise to get everything in sync. The overall process of doing all that is referred to as a Set-Up and it often goes together with changing the strings because changing the strings can impact those points.
That's what your guy meant by a Set-Up. It takes some time and expertise, so it's perfectly understandable and acceptable to charge for the service. Where I live, a Set-Up done by an expert can cost $75 or $100 (or more.)
The Set-Up of your guitar can be affected by many factors - changing the strings, the temperature, the humidity, getting a bang or shock, your own changing personal preferences and technique...
Set-Up/maintenance is applicable in different ways to most musical instruments. A musical instrument is a precision built mechanical device whose moving parts are subject to wear and tear from playing and from the environment, so certain parts need to be changed out, and a set-up of some sort is required from time to time to keep an instrument in good playing condition.
Some musicians take their instruments to an expert for a set-up every time the seasons change, because the changes in the weather change the set-up, requiring adjustment and "a fresh set-up".
He then stated that if we wanted them setup later, we could return and
we would notice the difference.
In all likelihood, he was telling you the truth. A good set-up can make a big difference in the sound and playability of your guitar.
Sometimes, less knowledgeable people will mistakenly find fault with a guitar or manufacturer because they don't understand set-ups. Often enough you'll find ratings like this when looking for an instrument:
One Star - when I unpacked it, the action was very high. Very hard to play,
didn't sound right - I had to send it back.
But a good set-up would likely have eliminated all those complaints. The guy might have sent back a very good guitar because he didn't know about set-ups.