What does one part in alcoholic drinks mean?

One part means "one unit of whatever you are measuring with"; they are used to ensure the right ratio of ingredients.

If you are making one glass (one drink) then "one part" is one shot, probably 1.5 oz or 4cl, depending on your jigger size.

Now, if you're making a jug full, like a pitcher of Margarita for example, you need to use the same proportions, or parts.

If you can't figure that out, just estimate the number of glasses you want to make and use your jigger.