Internal links are important to use because it helps the Google Spiders (what they call the programs that "read" websites and rank them for Google search results) know better what is on your site.
If a spider lands on a page on your site and no where on that site is there a link to another page, then that spider is done. But, if it links to another page and that page links to another then it creates a chain of information and that gives more for the Spiders to include in their findings, which can make your page results rank higher in a Google search. Does that make sense?
So, the menu on your page definitely helps connect links, but you still need something on each page that is linking to another page. You never know where the spiders are going to land! So, anytime you refer to something on another page link it up. Make sure to use the proper wording for links (called anchor text). <--See what I did there - I made an internal link for this blog. You will find in just writing your regular copy for your site that there will be lots on instances to link to other pages. Use all those instances and build yourself a better search engine page rank!