When PNG to JPG is the right move
PNG stores every pixel exactly and supports transparency; JPEG throws detail away to get small and has no alpha channel at all. That makes the conversion clearly right for one thing — photographs saved as PNG, which are often five to ten times larger than they need to be — and clearly wrong for another: screenshots, logos, diagrams and anything with text or flat colour.
The reason is what each format assumes. JPEG works by discarding high-frequency detail your eye is bad at noticing in a photograph. A hard black-on-white edge is nothing but high-frequency detail, so the compressor spends its budget badly and leaves visible ringing around every letter.
Quality, transparency and what cannot be undone
The quality slider trades file size against how much is discarded. Between 85 and 92 the loss is generally invisible at normal viewing size; below about 75 it starts to show in skies and skin tones. Whatever you choose is permanent — this is why the original is worth keeping, and why re-saving a JPEG repeatedly degrades it a little each time.
Transparency has nowhere to go, so transparent pixels are composited onto white before encoding. If your image needs to sit on a coloured background, that white box will show. Convert to PNG instead, or use image compression to shrink the PNG while keeping its alpha channel.