How to put vinegar in window sills and why?

Clean the tracks.

https://www.theintentionalmom.com/how-to-clean-window-tracks-like-a-pro-in-no-time-flat/

You can use a spray bottle, pour, or use a cloth or paper towels. I use a sponge and old toothbrush. Vinegar is an acid that can break down or dissolve oil and grease, dirt and dust, bugs and eggs, and other items that end up in the track over a period of time. Although I add a squirt of Dawn in almost any cleaning solution, the vinegar itself goes a long way into cleaning the tracks, drains, and a thousand other cleaning jobs. Best wishes!

Sprinkle some baking soda on them, then spray with vinegar. Let it sit a few minutes then wipe away the dirt and grime.

Put some baking soda in the sill then spray generously with white vinegar. The foam will loosen the grime and the paste is a mild abrasive to clean the sill.