I I am going from 4GB memory to 8 GB in a MacBook Pro. The new memory I purchased is listed as the correct memory for my MacBook.
My question is tho old memory states that it is 1333 MHz DDR3, the new 1066 MHZ DDR3.
To me, the uneducated computer novice, it would the lower MHz would indicate slower speed.
Does anyone know?

Yes 1066 Mhz DDR3 runs slower than 1333 Mhz DDR3. In practice you should not notice a difference. If your Mac is using Intel then the computer should automatically adjust to the slower speed.

You didn't say whether your new memory replaces or augments the old. I would not mix memory with different specs.

You didn't say whether your new memory replaces or augments the old. I do not mix memory with different specs.

Jim, yes the computer uses Intel.
Matt, the 2 old 2GB memory sticks are being replaced with 2 new 4GB for a total of 8GB.
Actually the computer belongs to my wife and the Apple Store recommended the upgrade.
I recall a few years ago when replacing memory, I was sent memory that was supposed to be
the correct upgrade but did not work.
In that case and on a different MacBook, when restarted would beep and not boot.
No harm done and reinserting the original memory, the computer once again worked.
I’m hoping this the case when I attempt the switch.

That’s good. I did the same thing to an older Mac I have. Having 8 stopped all the beach balls.

I did the upgrade yesterday and it was a 10 minute job.
The computer is working extremely well.

Nice,

Glad to read the upgrade went well.

It is my wife’s computer and after 55 years of marriage it’s sometimes difficult to impress her......
but this did it!

That makes life MUCH better. When the wife is impressed, that's all that matters.