What is a template or theme?
A website template or theme controls the "look and feel" of a website. Different platforms refer to one or the other, but they mean the same thing.
A template/theme includes all of the formatting to control things in the website such as layout, where the logo sits, where the menu(s) are and the style of them, as well as the site font(s), colour scheme, etc.
Theoretically, you can change a template/theme on a website to give it a new "look and feel" without affecting underlying content (although this depends on the template/theme already in use).
Some solutions providers develop their own templates/themes, but all website platforms have professional template/theme clubs and this is a more cost-effective option in most cases.
Once we start a project, one of the first questions we'll ask is for you to provide some existing websites you like, perhaps competitors or just a favourite business. This helps us get a feel for the type of "look and feel" you like. Once we get this information, we'll provide you with some suggested templates/themes in whichever platform your site is going to be built in.
What To Look For
The most difficult thing for most people when looking at template Demo sites, is to visualise it with their own words, colours, photos and logos - it's really hard!
The rule of thumb is to try to find a template/theme which is mostly similar to what you're visualising for your own site. While most things can be changed, the more changes that are required, the longer it takes and the more it costs.