You could think of the sites that share your server as your roommates; there's really not that much separating you from them. Sure, you can close the bedroom door, but they can still cause nightmares for you in the kitchen and the bathroom. In web hosting terms, all the sites share a single server's resources, so huge traffic spike on Site A may impact the neighboring sites' performances. It's even possible that another site could take down the shared server altogether, if it crashed hard enough.
On the plus side, SiteGround offers free automatic daily backups, access to the Cloudflare CDN, high-performance SSDs for all plans, unlimited email accounts and integration of the free LetsEncrypt SSL certificate into sites. The company does limit bandwidth and storage, but even those who claim to offer so-called unlimited bandwidth and storage really have some limits in its terms of service.