This question is occasionally asked.
The question is a can of worms. It brings tens of different responses, as 아리랑 implies many and much.
The simplest, yet probably unsatisfying answer to your question: 아리랑 is a name of the pass.
Understanding what 아리랑 is and why the word is used to name the pass leads to deeper understanding of these very cultural folk songs.
One of the claims regarding the origin of its word is 아리다 and 쓰리다, but that is not all that it means.
아리랑 can imply both extremities: good and bad, the sun and the moon, yin and yang, desperation and uplifting hope, the power and the oppressed.
For that reason, while you will hear 아리랑 songs in a minor tune, delivering deep sorrow and helplessness, you will also hear different 아리랑 songs with jubilant upbeat hopeful tunes.
Because of the hardships that Korea has gone through, and also because the 아리랑 has been a word the oppressed and repressed used to express themselves, the word often means more minor than major. Regardless, it means both. For instance, in the song:
아리랑, 아리랑, 아라리요
아리랑 고개를 넘어간다
나를 버리고 가시는 님은
십리도 못 가서 발병난다
아리랑 pass represents the sorrow, pain, loss, desperation, etc. that the singer has: the singer's sorrow his/her lover is about to step on, go over, and leave them behind. It represents the singer and what he/she endures as the lover leaves. But at the same time, it represents the hope that something will stop the lover from leaving them, a force that will help their love continue, the joy and happiness of being together again.
The 아리랑 is also used to simply state the joy. At the harvest time, the word 아리랑 would be used in the song to hay how happy the farmers were and give thanks to the heaven. The community band would be formed, singing joyful 아리랑 song and the neighborhood joined in the march for a bigger festival, singing 아리랑 song.
아리랑 has yet been defined in even Korean dictionary. Understand it as an expression, just as hooray, alas, presto, or yahoo. It implies unspoken and unsung stories that words cannot describe all. Bitterness, sorrow, pain, torment, loneliness, repression, and all the tolerance necessary to survive the moment are implied in this one word. Also, hope, joy, excitement, happiness, explosive pleasantness, and all the good things are implies as well. Hence, 아리랑 is known to be the word that represents Korea, its culture, and its history.