The carousel on the Roots theme is designed to span the full width of the browser on all screen sizes. This means if your image isn't as wide as the visitors screen it will be stretched to fill in the remaining space.
To determine the ideal image size for your carousel the key piece of information to consider is screen size. There are lots of resources for finding these kinds of statistics but according to https://gs.statcounter.com/screen-resolution-stats (at the time this article was written) the two most common desktop screen sizes are 1366px with a usage of 9%, and 1920px with a usage of 8%.
Considering that the same image will load on desktop computers and mobile devices, it's also important to not upload an image that's too large as that runs the risk of slowing down mobile load time. With that, we recommend your images be no larger than 1920px, ideally we recommend creating them around 1400px wide since the percentage of users viewing your store on a screen larger than that starts to become less and the image is stretched to fill the screen.
The height of the carousel images can be tailored to what works best with your images and site design. We also recommend making all of your carousel images the same dimensions for the best visual experience.