I see this question come up a lot so here's a quick reference. I put this together while building a yarn search tool and learning from experienced knitters and crocheters along the way.
Cobweb : finest, ultra delicate lacework, not for beginners
Lace : shawls, doilies, lightweight wraps, slow but stunning
Fingering : socks, shawls, colorwork, most popular for indie dyed yarn
Sport : baby garments, lightweight sweaters, underrated sweet spot
DK : stands for double knitting, super versatile, sweaters and hats
Worsted : most commonly used weight, best for beginners, works for everything
Aran : between worsted and bulky, named after the Aran Islands, great for cables
Bulky : thick and fast, winter hats, cowls, quick blankets
Super bulky : even thicker, you can finish a hat in one evening
Each weight has specific gauge ranges and needle sizes. Happy to share more detail if anyone wants it.
Also if anyone's looking for yarn, I built skeinscout.com where you can search across indie dyers and filter by weight. Free to use.