The song's narrator (Levi Stubbs for the Four Tops, David Ruffin for the Temptations) asks his love, who's leaving them, to allow him "one last look" at her so that he'll always have memories of her.
In The Temptations' case, they were one of the few major Motown acts never to release a single produced by the trio, due to (previously) Berry Gordy, Jr., Smokey Robinson, and (then currently) Norman Whitfield having a tight hold on the group's released material.
Brian Holland and Lamont Dozier had to in fact fight for the chance to produce "Just One Last Look" for the Temptations, and Whitfield successfully blocked its release as a single.
This song would go on to be released as an album track on "The Temptations with a Lot o' Soul".
This was recorded around the time H-D-H decided to give both them and The Supremes a harder edge on their songs.