Puncture resistant tubes, sometimes called thorn proof, have an outer wall that is three times as thick as a standard tube (see the cross section photo) and this extra thickness dramatically reduces the risk of puncture.
In our experience they will decrease your chance of getting a flat by more than 95%. They also hold air much longer than standard tubes, usually only needing to be inflated once every 6-8 weeks.
The downside is they cost and weigh a little more.
They typically weigh around 200g more than a standard tube, about half a pound per tube of additional rotating mass on your bike.
But, unless you are trying to keep your super light bike as light as possible for competitive riding, using puncture resistant tubes (and tires) practically eliminates ever getting a flat on a ride.
Because they are so durable these tubes are also the best choice for heavier and difficult to change e-Bikes, for kids jumping around on bikes, and for older 70s and 80s road bikes with 26x1-3/8 or 27x1-1/4 steel wheels.