On a shared server, your site is vulnerable to the company it keeps. A bad 'neighborhood' may result in your shared IP being blacklisted, and that could result in your sent emails being filed into spam folders. You can guard against this by using a VPS or dedicated server, or using a third party email service that is separate to your hosting service.
Shared hosting is web hosting in which the provider houses multiple sites on a single server. For example, Site A shares the same server with Site B, Site C, Site D, and Site E. The upside is that the multiple sites share the server cost, so shared web hosting is generally very inexpensive. In fact, you can find an option for less than $10 per month.