What is the therapeutic index and what is its clinical significance?

I remember once being told by a pharmacist to be careful with certain meds because the “safe dose” and the “dangerous dose” weren’t that far apart. That stuck with me, and later I came across the term “therapeutic index.” I kind of get that it’s about the balance between effectiveness and toxicity, but I’m still not clear on what it really means or why it’s so important in practice.