Having a Dedicated ip is good mainly for the purpose of your email, especially if you are sending out larger quantities of email's (Which you should use a Provider like Sendgrid if you are). If you do not send alot of email's but want to be sure your email's are not blacklisted or sent to spam get a dedicated ip or use zoho for your websites email accounts.
Other than that at this point there is not much need for a dedicated ip, you previously had to get one for an ssl certificate but most hosts support SNI which allows you to have an ssl certificate on a shared ip address. And some "SEO Experts" said it is good to have for SEO purposes but that no longer matters any longer. Especially with the shortage of IPv4 Address' google changed the way their algorithm works so most seo hosts went out of business.
Dedicated IP address refers to the IP address that is solely dedicated to your server and is unlike shared hosting services. VPS and dedicated servers are those that offer dedicated IP address for your services.
Good for emails, also required if you want a pure SSL cert. to your domain and not one through a CDN (such as CloudFlare). Others use it for using programs such as IRC or having software check if a license/key is correct, etc.
Modern versions of cPanel/WHM actually don't require a dedicated IP for SSL certificates, although as others have said, it can help you get through spam filters in some cases, or if your host's software stack only supports dedicated IPs for SSL.
All other comments are correct. Some resellers may also want dedicated IP addresses to conceal the fact that they are reselling (although you can create custom nameservers from your provider's IPs)