Use the phrase where change might lead to trouble or complications in a situation. Your garden is thriving; better leave well alone and not add new plants.
Pro Tip 2/3
Risk Awareness
Apply the phrase when it's risky to alter something that's already satisfactory. The contract looks good as it is; we should leave well alone.
Pro Tip 3/3
Subtle Warning
It carries a mild warning against potential negative outcomes of unnecessary action. Her temper has cooled down; let's leave well alone now.