Hmmm... I'm not sure about "something or the other," but if it's the same as "something or other," which we say all the time around here, we use it when we don't know what something (usually an object) is, and it's not essential to know for what we're communicating. For example, if I'm telling someone about what happened in school yesterday, I might say, "The student had something or other in her hand, distracting her from her work, and no matter how many times I asked her to put it away, she refused." In this case, the refusal to comply is the point of the story, not whatever she had in her hand. It could have been a cell phone, a mirror, a note, or anything, and it's not worth spending time trying to guess because it's not really essential to know.