The temperature-dewpoint spread is the difference between the temperature and the dewpoint. Great, so what is the dewpoint exactly and why does this matter?
The dewpoint of a parcel of air is the temperature at which an air parcel would need to be cooled to become completely saturated with moisture (a cloud would form, or in more proper terms, the air can no longer hold the moisture). Remember that the warmer the air, the more moisture it can hold in gas form (as we cool the air without removing any moisture from it, the air becomes saturated with moisture).
Bottom line, if the temperature and dewpoint are far apart, the air has to be cooled a whole lot before it becomes saturated (meaning there isn’t much water or moisture in the air in the first place). If the temperature and dewpoint are close together, then the air has lots of moisture in it. If the temperature and dewpoint are the same, then you likely have fog, low visibility, lots of clouds, etc since the air is saturated and now the moisture that was a gas is becoming a liquid (and visible).
The air gains moisture through two processes, evaporation and sublimation. Evaporation is when water goes from a liquid to a gas, such as a puddle on your driveway on a hot summer day that “evaporates”. Sublimation is when water goes from a solid to a gas, such as when snow or ice “sublimates” and adds moisture to the air without going through the liquid phase.
You depart on a clear VFR late afternoon for a destination that is forecast to be VFR at your time of arrival (your time of arrival is just after sunset). You note that the current METAR shows only a 3 degree difference between the temperature and dewpoint, but that means nothing to you because you had not yet taken this course. As you approach your destination airport you listen to the AWOS only to find visibility has dropped greatly and there is fog around the airport. This fog appeared due to the moisture in the air (and the air being nearly saturated already with that close temperature dewpoint spread) and the ground radiating its heat, cooling itself as well as the air just above ground level quickly as the sun disappeared for the day. You now will now have to divert to another airport as landing with a low layer of fog on the runway (even if you can see through it from above) is extremely dangerous and would likely result in a significant reduction of forward visibility and an exceedance of VFR minimums upon entering the fog.