"It was Mary I saw" emphasizes who you saw. It means your listener already knows that you saw someone.
If I asked you "Who did you see at the station yesterday?" you might reply "I saw Mary", or "It was Mary". If I asked you "Did you see Bill at the station yesterday?" you might say "No, it was Mary I saw."
But if I asked you "Did you see anyone at the station yesterday", it would sound a bit strange to me if you replied "It was Mary I saw", because I wasn't asking actually asking who you saw, just whether or not you saw anyone.
"I saw Mary at the station yesterday" doesn't emphasize who you saw, where you saw them, or when.
edit: actually, on reflection, this doesn't answer your question at all. We're really interested in the difference between
It was Mary I saw at the station yesterday
It was Mary that I saw at the station yesterday
The word "that" doesn't change the meaning of the sentence, and you can drop it out. It changes the tone a little bit, making it sound a bit more precise or formal, but it doesn't affect the meaning.