According to the Collins English Dictionary, a Season is defined as :-

                                              NOUN, One of four divisions of a year etc etc.

So, could someone please explain why the Americans refer to a series of TV programs as a Season.

A Season is when you freeze to death, stuff starts growing out of the ground, your skin peels off, followed by, the stuff that grew out of the ground dying.

Therefore, it's a series not a season, it's not difficult. 

Rant over.

In France (I know, we're supposed to speak French, lol), we use both:

La série "24", saison 3     (the serie 24 season 3)

Just an example. I loved 24, but not all the seasons.

Much as I love to rant at the use of language from our USA cousins, in the case of 'season' I think they have it right.
In UK when they say 'new series' on TV do they mean a brand new series or a new season of an existing series?
A new series is exactly that in the USA. A new season is a new set of episodes for that series, which is normally released at the same time of year or 'seasonally'.

I'm sitting firmly on the fence here.

But I would add this:

Top Gear has just finished a series, at the end of the last program the presenter did say "That's the end of the series" if he had said "That's the end of the season" the statement would have been incorrect, or would it? Isn't spring here now?

Looking forward to the next series of Top Gear in the summer season.