With extract, you add the extract to the boil and create wort.
With partial mash (aka mini-mash) you steep crushed grain at a precise temperature for a precise amount of time (like 152 degrees for 60 minutes). This allows the malt starch to be broken down to fermentable sugars. Then heat sparge (rinse) water to a specific temperature (say 170 degrees). Lift the grain bag out of the kettle, pour the sparge water through the bag and collect it in the kettle. This is wort; get it to a boil and it's identical to extract brewing from this point onward. Partial mash adds about 90 minutes to your brew day.
In a partial mash you use crushed grain to obtain some fermentable sugars, then boil this and combine it with extract, add hops, etc. Sort of like steeping grains, but not exactly like making tea. It's an intermediate technique between extract and all grain.