Some of the non-English versions of the title translate "edge" to mean "limit" or "border". Seems fine to me.

"Edge of Tomorrow" is not a common phrase. It has a specific reference to the movie (which I have not seen). As far as I understand it means 11:59pm (so literally on the edge (=boarder) of tomorrow, as Olivia suggested. I think you will have to watch the film to fully understand the title.

Usually if an English speaker says on the edge of ___, it can mean a couple things. There is an idiom in English "to live on the edge" and it means to live dangerously. On the edge can also be used very literally, as in the border or end of an object, for example you could say "he sat on the edge of his bed." In this title I believe what s most likely meant is on the border so it would mean that it is the border of tomorrow or it's "almost tomorrow."