An electrical outlet will not power a lamp. The appropriate circuit breaker is fine. The outlet itself has been replaced. A test with a multimeter gave a reading a reading of 95 volts AC at the leads. What is wrong with this circuit?

Impossible to say with a crystal ball. You need to do some troubleshooting.
Remove each device on the circuit and check splices and connections.

Even with a bad connection or loose wire, 95VAC, which is indeed low, should power an incandescent bulb.

How did you get the 95V reading?