An IP address is like a phone number for a computer on the internet (simplified), and this computer can serve many functions, such as hosting web pages, email servers etc. A domain name is a unique individually owned alpha-numaric name which is used to indentify a computer on the internet (Web Sites, Email Servers, IRC servers etc). A domain point (such as yahoo.com) points to a computers IP address such as 188.8.131.52. Since people remember letters better than numbers, it's a way to make internet usage easier for everyone.
To answer your question:
No, you will not need multiple IP(s) per domain. Today hosts have the ability to offer shared IP technology, in which multiple domains can be hosted on the same IP. There is really only a few reasons to need a dedicated IP for a domain, and otherwise you would have no performance difference. Those reasons you might want another IP is if you want to run a secure server, anonymous FTP, or a custom nameserver. Otherwise, you will not need multiple IPs.
Old man of the hosting world..