WordPress is not just about blogs. Widgets and plugin are like apps that install into your WordPress site to enhance its functionality and take on any site on internet! For them to work properly, the WordPress template needs to be setup correctly or they will simply not work. All WordPress templates has widget positions where the widgets are displayed. In all likeliness, your old site design is not made with WordPress in mind.
So when we convert your current website to WordPress, the first thing we do is, we transform your site's design into something that "works" with WordPress. This means your design becomes a WordPress template with a new layer of code that makes it WordPress friendlier. Once we deliver the site to you, you will be able to install widgets and plugins just like any other WordPress site built from scratch.