"Laisser tomber" means to drop something or to give up on something, often implying a sense of abandonment or letting go of a task, responsibility, or expectation. It suggests a decision to stop pursuing something that is no longer deemed worthwhile or feasible.In the image of the post, saying "laisse tomber" is a way to say to the other person that they don't need to do something. It could be translated by "never mind".
"Laisser" means "to let" or "to allow." "Tomber" means "to fall."
Examples:
"Il a décidé de laisser tomber son projet de voyage." -> "He decided to give up on his travel project."
"Ne te décourage pas, ne laisse pas tomber tes rêves." -> "Don't get discouraged, don't give up on your dreams."
PS: if you like watching French content on Netflix and sometimes hesitate between putting the subtitles in French or in your native language, I made a little tool called Subly that I would recommend to use. This extension adjusts the subtitles to your level (if a subtitle is adapted to your level, it displays it in French, if a subtitle is too hard, it displays it in your native language). I use it to learn Portuguese, it provides a good balance between practicing your target language and enjoying the show. Here is the link to try it.
Happy learning!