Parallel motion is when two voices (vertical on the staff) form a given interval in relation to each other (eg a 5th), then move to the same interval (a 5th) in a different pitch.
So:
G C
C F
is parallel motion, in this case parallel 5ths, since you have a 5th (CG) followed by a 5th (FC).
When you add the 3rd, you're adding parallel movement, but in the form of parallel 3rds, with a major on the bottom and a minor on the top (CE, EG to FA, AC)
As a general rule of thumb, parallel movement is avoided (particularly parallel 5ths) simply because it sounds "boring." But any rule, especially in music, can be broken on ocassion if it's right for the moment. Do what sounds best to you, just don't go overboard...
Hope this helps...
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