Teflon tape, also known as Plumbers Tape, is a wonderful thread sealant that can be used to reduce the chance of leaks when connecting threaded plumbing fittings. Instead of being a gooey liquid, it is neatly contained as a tape on a spool! Since it is a tape, there will always be a starting and a stopping point. This is where the confusion can begin!
When you wrap Teflon Tape on threads, you want to wrap with the threads heading towards the head of the screw. If you wrap the tape in this direction, it will stay in place as you tighten the fitting and form a good seal.
If you forget and wrap the Teflon Tape against the threads, it runs the risk of not sealing as well as it could. When you tighten the fitting, the plumbers tape will actually be pushed out of the way by the female threads. Since they are pushed away, they are not present to form a good seal and leaks can ensue.
What does "with the threads" mean? Lets look at a picture:
You can see how the tape is wrapping up the fitting in the same direction as the threads. This means that it will lay into the threads and cover any voids that might allow a leak to occur. You might also notice that I do not tape the first few threads at the end, there is a specific reason for this.
When you go to thread the male fitting into the female fitting, you run the risk of crossing the threads. If the threads are clear, you will know when you are properly lined up because it will thread in with ease. Once it reaches the taped threads, you know everything is aligned and you are ready to proceed with tightening down the fitting.
Lastly, you only want to do a few wraps with plumbers tape. If you wrap too much tape: the threads will disappear, you will waste materials, and you won't be able to tighten the male fitting that far into the female fitting. It is best to only do a few wraps, keeping the tape thin and light that way the threads can do their job and the tape is merely there to help seal up any gaps that could create leaks.
Next time you need to thread some plumbing fittings together, be sure to use some plumbers tape, leave the first few threads exposed, and do a few wraps tightly with the direction of the threads of the male fitting.