What artist inspired the meaning behind "Out of the woods" By Taylor Swift in 2014 on her album "1989"? (please explain) ..

It was Harry Styles.

Explanation:

1. "We were built to fall apart/ Then fall back together"

This lyric implies an on-again, off-again relationship, which -- based on the amount of tabloid headlines the brief romance generated -- definitely seems accurate.  

2. "Last December..."

While Swift's most famous December-related paramour was Taylor Lautner (See: Her missing his "tan skin" in "Back To December"), this clue could also point to Harry. The two allegedly had a big fight in December 2012, which ultimately led to their breakup (and Swift's super-sad solo boat ride).

3. "Remember when you hit the brakes too soon/ Twenty stitches in a hospital room"

Remember when Swift and Styles went snowmobiling together in a much-publicized trip to Utah with Justin Bieber? Rolling Stone wrote about these lyrics: "She says it was inspired by a snowmobile ride with an ex who lost control and wrecked it so badly that she saw her life flash before her eyes."  

4. "Your necklace hanging round my neck/ The night we couldn't quite forget/ When we decided/ To move the furniture so we could dance/ Two paper airplanes flying, flying"

While the duo were rumored to be together, the two wore identical plane necklaces.

the previous answer given.