A raster image (JPEG, PNG, GIF) is a grid of pixels. When you scale it up, the pixels get bigger and the image gets blurry. A vector image (AI, EPS, SVG, PDF) is math — points, curves and colors — and it stays sharp at any size.
Print shops need vector artwork for anything that will be enlarged, spot-color-separated, laser-cut or embroidered. A blurry raster of your logo cannot be turned into a clean screen-print film without being redrawn.
'Auto-tracing' — the one-click Illustrator function — turns a raster into a vector-shaped mess. The curves are noisy, the corners are jagged, and the colors are wrong. A real vector conversion redraws the artwork by hand, matching your original curves, matching or replacing your typography, and delivering clean editable files.
If your only copy of your logo is a JPEG from an old website, that's normal — most brands are in that position at some point. A vector conversion service takes an hour or two and gives you back a permanent, editable, print-ready master.