First let's start by what is an IP address. It is a unique sequence of numbers separated by dots that identifies each device using the Internet to communicate over a network. The server where your website is hosted also have an IP address that identifies it and in the case of shared hosting, there can be many domain names connected to the same IP address.
Dedicated IP address in a web hosting means that the server will assign a specific number that will be used only by you and your domain name. An example how this works you can see in the image blow.
Dedicated IP address
Do you need one? There are a few reasons that people might want a dedicated IP for their domain.
1) One case is if you want to use an SSL certificate and it needs a separate layer to identify the identity of your site.
2) Another reason is if your website have a lot of traffic and you want to maintain it faster and reduce the chance of a crash and timeouts for your users. This is why a dedicated or cloud hosting is preferred when you expect high volume of visitors.
3) The third major case is for SEO reasons. If you are worried that there are a lot of spammy sites hosted on the same server and IP as yours and you want to separate yourself from them. More on the topic is explained in this video. And to check who else is hosting sites on your server, you can use service like www.my-ip-neighbors.com