I am replacing an outside lamp. The hot and common wires each have 3 wires (braided type) that are capped together along with one wire going to the lamp. What is the meanng of the 3 strands wired to the hot and the common?

Can you get just a little more vague?

Guessing, If your light is in the middle of a branch circuit you will have 1 cable (black/white/ ground) as the feed or supply, 1 cable (black/ white /ground) to the down stream circuit and the wires from the light fixture.

If there is a switch loop, you will have the feed cable black, a white conductor (should have black tape around it or marker) connected to the feed and a continuation black all capped together.

All of the whites including the fixture white should also be connected together.

The black (return from the switch) should be connected to the black from the light fixture.

Those are the easiest connections to have, however, there are a myriad of other possible connections so either append a picture using the "Go Advanced" button or please give us more information.