If the weather says winds are 15mph NW does that mean the winds are headed NW or coming from the NW?

Winds are out of the north west.

It is, of course, a convention coming from seafarers of the past but international Search And Rescue conventions agree that:

1) the wind is always given as the direction it comes from,

2) a sea current is always given as the direction it goes to, and

3) a position is always given relative to a reference. For example, you must say: I am north of the lighthouse and not, the lighthouse is south of me.

Back to the wind: In aviation, the weather forecast called TAF writes e.g. 25005 which spells: the wind is two-five-zero at five knots.

It means they're coming OUT of the NW...so they're blowing Southeast.

The wind direction stated in any forecast is always what direction they are coming from.