Zotero supports online syncing, so you can access your Zotero library on any computer with internet access. Zotero syncing is split in two parts: data syncing and file syncing.
Groups provide a powerful way to share collections with a class, work closely with colleagues on a project, keep track of conversations in your field more broadly, and keep tabs on what people at your institution or in your department are working on.
There are two ways to create Zotero groups:
More on groups from Zotero.