Answer: Points are used to trigger the ignition coil to fire at a precise time, assuring that full voltage is available to each spark plug as needed. The bad thing about mechanical points is that they degrade from ordinary wear and tear as well as electrical arcing, necessitating periodic replacement. The good thing about mechanical points is that replacement is simple and inexpensive, and is usually done as part of a routine tune-up, making complete failure a rarity. Even better is that fact that in the unlikely event of a problem, a simple “road-side cleaning” is usually all it takes to get you home.
There are quite a few systems on the market that are designed to replace the mechanical points system with an electronic system. The advantage of these systems is that they trigger the ignition coil electronically rather than mechanically, thus eliminating parts that can wear out from ordinary use. The most popular system is probably the "Pertronix Ignitor.” The good thing about this system is its low cost, ease of installation, and reliability. The bad thing about this system is that if it should fail, you will have to be towed to your destination. There are no “road-side remedies” other than keeping a set of mechanical points in your glove box in case the need arises to install them.
I’ve installed many Petronix systems on boats because the salt water environment tends to significantly shorten the life of mechanical points. Unless the mechanical points in your car are particularly troublesome, I don’t see any reason to change them.