Without the transmission, your car won't move. The motor provides the power, the wheels provide the motion, but without the transmission, the power from the motor won't get from there to the tires.
The transmission has a series of gears that it goes through in order to transfer power from one place to another. It doesn't matter if it's an automatic or manual transmission, the way it works is basically the same. A clutch gets activated, and the gear changes from one to the next. The clutch is basically a neutralizer that disengages the gears when it is activated so that the gears can change without damaging anything. That's why you hear a bit of silence when the gears shift. When the clutch is let go, the gears are re-engaged and the gear has changed, whether up or down. The biggest difference between a manual and an automatic at that point is how the clutch is engaged. With a manual, you push a pedal that does it, in an automatic, there's a sensor in the transmission that does it. The fact that your transmission gets power from point A to point B means that you need to make sure that you get any problems fixed so you can continue to get from point A to point B. So, what are some things that you should look for in order to know you have a problem?
Pause Between Gear Shifts
If you notice that there is a small pause between gear shifts and the gear feels like it is having a hard time slipping into place, it could be that the particular gear has started to wear out. The gears have teeth on them that mesh together. As those teeth mesh together, the gears can spin, sending the power from the motor to the drivetrain and out to the wheels. As a gear wears out, the teeth can wear down or break off, which can cause the gears to not mesh well when the gears change. That's what causes the pause between gear shifts. If you have a manual transmission, you might feel where it tries to catch as you shift, but it just misses by a smidge.
Without a transmission, it doesn't matter how good your tires are or how powerful your motor is because you aren't going anywhere. That's why it's so important to make sure that your transmission is in good shape.