I've always been confused about this topic and was never really able to undestand it.

In layman terms can someone explain to me what "swingweight" actually is and how a d3 is different than a d7, etc?
Bringing this up because my clubs were built at a d3 swingweight. The Miura wedge I won from Frank has a SW of d7 and not sure what that actually means.
As others have already posted explaining swingweight, I'll add a little to the subject.
Swingweight was the first method devised in an attempt to "match" clubs within a set. Kenneth Smith developed the system by balancing a club on a 14" fulcrum and creating a scale in which to measure a value of each club. When he measured most clubs of the day, they came out right around D2 on his scale. So that became Smith's "standard." Smith's theory was if the clubs were all balanced to the same value on the swingweight scale, then all the clubs would feel the same during the swing.
Then along came a couple of other methods. Frequency matching and then Moment of Inertia (MOI) matching. Frequency matching was an attempt to create a consistent frequency slope from one club to the next in order to ensure the "flex" of the club was consistent. The problem with frequency matching is that usually the butt end of the club is clamped into a frequency counter that measures oscillations per minute. In reality the resulting frequency is only a presentation of the "butt" frequency of the shaft and not the entire flex profile throughout the remainder of the shaft.
The best way to now match clubs is by Moment of Inertia (MOI). Without getting too technical, Moment of Inertia as it relates to the golf club and the swing is a measurement of "how easy" or "how different" it is to set an object in motion around a defined rotating axis, the player would be the rotating axis. You can visually see this in ice skating. When a skater "spins" on the ice with their arms close together, they will spin very quickly (Low Moment of Inertia). As they extend their arms outward, they begin to slow down (High Moment of Inertia).
Finding a club that feels comfortable and is easy to hit is the key to MOI matching. I think everyone's had a club in a set they had complete confidence in and were able to hit consistently. It's possible to measure the MOI of this club and duplicate that MOI "value" in all the other clubs in that set. So you if found a club you were absolutely in love with....how it felt when you held it, how it felt when you swung it, how it felt when you hit the ball and you were pleased with the result of the shots....it's possible to duplicate the values that contribute to the Moment of Inertia of this club when
you swing it. If you made a set of clubs with the same MOI values, the set would be MOI matched to
YOUR specific swing. These values are unique to you alone. That's why early attempts to mass produce "MOI" matched clubs failed (I believeTommy Amour was the first company to try MOI matching). The process failed because a single MOI value does not fit everyone. Everyone will have a unique MOI value that will work for them.
Does it take a Physics degree to MOI match golf clubs? No. If it weren't for specialized equipment it would certainly require someone with a strong back ground in physics to accomplish MOI matching. But because their are MOI counters and associated software developed for the specific purpose of MOI matching golf clubs, it's not a difficult process, if you have the equipment. Most clubmakers have invested in the equipment necessary to perform MOI matching. All the complicated mathematics required to properly compute correct MOI values is accomplished by incorporating the values measured by the MOI counter into the software.
How do swingweights shape up in a properly MOI matched set? Swingweights increase gradually from the longer irons to the shorter irons. Remember, swingweight is not actually a "weight", it's more of a measure of balance on a fulcrum.