As Bonnieee has mention it could be indeed left and right. 우(右) 오른쪽 right side. 좌(左) 왼쪽 left side. Chinese letters 한자 (漢字) Please be aware that there is a lot of words and letters with a Chinese origin! :) You can use Naver to find meanings or download a cellphone app to help you learn hanja! 감사합니다 인재덕

Not sure if I am understanding the situation right, but I am guessing there's A and B side by side and when asked to pick one, by saying 우/좌, it's probably indicating his choice by the position of A and B so inside of answering using "A"/"B" . It's a bit like when I hold rubber in one of my hands and ask you which hand do you think has the rubber. Left 좌? or Right우?

On the video you mentioned, I believe he is just indicating he cannot decide. He is just reading the two choices [강소라, 고아성] prefixed by their position, [좌소라, 우아성]. The choices here are names of actors, so he probably wants to avoid saying who he likes more. 좌 and 우 doesn't really have any special implication beyond those well known in English and other languages too, like the right hand side being associated with the correct side. Just as "right" means both the right hand side and "righteous", the native Korean word for 우, "오른편 / 오른쪽", has the same association - 오른 comes from 옳은 = 옳다 = right/correct/just. There is another word "바른", which is like both 오른 and 옳은 merged into one. Plus, 좌 and 우 means the same left and right wing in politics as in English.