Push mower... could you be any less specific, or mebbie a bit more vague?
There's Briggs, Honda, Kawasaki, Kohler, Robin, Tecumseh, Lawn-Boy... all making engines for walk-behind mowers... and probably a hundred or more brand names using one of those engines... and everyone one of them has an ignition system.
The magneto systems used on many engines, and many of the aftermarket replacements, use an integrated magnetic trigger (a hall-effect transistor usually) in the magneto assembly. When the flywheel magnets fly by, the field in the magneto windings build, then the magnet is detected by the hall-effect transistor, which is connected to a power transistor of some sort, which does the same function as contact points... shorts the windings, causing field collapse, thus, spark voltage.
If you post a picture of the engine, with magneto assembly in place, we could tell you what type it is, wether it's OEM or aftermarket, and probably more...
But the answer to "how does it work":
It works great. No points to wear out, no separate module to fuss with. When it goes bad, replace the whole thing, clean the flywheel magnets with a piece of 120-grit sandpaper, and use same sandpaper to set gap for module, and put it back together.
I love you too! Dude why get your knickers in an uproar? If it has a coil and the flywheel has magnets Im pretty sure its going to work like the fella that didnt get all bent out of shape says. Now please pick your panties out of your crack and relax, please.
Actually, the pushmower has an extremely complicated ignition system, with a fuel requirement quite unlike most mowers.. meat and 3 veg is a good start... but also needs motivation to start.. like someone telling you to get out there and get that lawn cut.