This is the 3680th most frequent Swedish word.
glimt
Glimt: A glimpse or flash.
In this sentence, "glimt" refers to a spark or slight sign of an emotion or quality.
Hans ögon hade en glimt av lust när han tittade på henne.
His eyes had a sparkle of desire when he looked at her.
"Glimt" is used metaphorically here to signify a small or faint indication of hope.
Det var en glimt av hopp i hennes leende.
There was a glimmer of hope in her smile.
Here, "glimt" is used to indicate a brief view or sight of something, specifically the sun.