Ok, let's try this again. Simpler terms.
When shifting down into a lower gear the engine speed needs to go up.
You can twist the throttle to raise engine speed to the point that it should be when selecting the lower gear.
Example: Without blipping/rev matching
You are in fourth, spinning 5000 RPMs. You want to shift into third.
Pull in the clutch, the trans goes into neutral. The RPMs drop.
Select third, the RPMs need to shoot up to 6500 RPMs.
You get a jerk.
Now with blipping/rev matching.
Pull in the clutch
Select thrid gear
Blip throttle (twist throttle very quickly so that RPMs shoot up)
Let throttle out.
No jerk, all smooth
All done very fast.
Clutch/gear/blip/clutch.