편 does mean side or direction, but it also means inclination or tendency as in the example you gave. face tends to look young... looks youthful..
The pattern here is Verb stem + ㄴ/ 는 편이다
날씨가 떠운 편이다 It tends to be hot (here). It is rather hot here.
그는 좀 뚱뚱한 편이다 He is on the fat side. He is a bit fat.
You can use this pattern with action verbs.
그는 다른 사람에 비해서 영화를 즐겨 보는 편이다 He tends to enjoy movies more than most people. He tends to enjoy movies.
그는 친구가 많은 편이다 He tends to have a lot of friends (compared to others.)
I hope this is helpful.