For the functionally identical enemy in Spelunky 2 that is different in appearance and name, see Hang Spider.
Spinner Spiders reside in webs attached to the ceiling, and will periodically dive downwards on a silk thread before climbing back to their nest, akin to a person performing a bungee jump.
They only ever move vertically, and can control how far they drop based on where the Spelunker is. They are easily dispatched with well-timed attacks.
Their webs can cause issues in a Speedrun and will leave projectiles stuck in them even if said projectile kills the Spinner Spider residing within.
Spinner Spiders also appear more frequently in the Spider's Lair Level Feeling.
If you try to move a Spinner Spider whille it is lowered by moving a crush block into it, it will stay in it's current animation and not move. This does not always work, however, as sometimes the Spider's web will just break.