You get a spark (from a spark plug) when the points open. That breaks the circuit in the coil's primary winding which causes its magnetic field to collapse. That generates high voltage in the secondary winding, that can jump the sparkplug gap - with a spark.
You can test that bit by disconnecting the black/white wire to the distributor and earthing it on the engine. You'd get a plug to spark when you lift the wire off "breaking the contact" - provided the ignition is supplying leccy to the +ve terminal on the coil and the rotor arm is aligned with the plug you're looking at. You can get round the last bit by attaching the plug lead directly to the coil.
If that gets you a spark, but the distributor doesn't, then the distributor isn't "breaking contact". That could be because the points aren't making contact in order to be able to break it or there's a short that earths the coil whether or not the points open.
That could be the wiring touching the dizzy body before the points or a failed condenser leaking to earth.
The condenser is a capacitor that stores charge (like a very rapid discharging battery) close to the points. That charge jumps the points gap the moment they come close enough, reducing the amount of time the points can arc & burn. It also makes the coil's primary field collapse more rapidly giving a brighter spark at the spark plug.
The simplest test for the condenser is to replace it with a known good one - it's always handy to have ignition spares anyway.