#colophon h2.widget-title

If you’re referring to the accent ‘stripe’ behind many elements like widget titles, and you want to make that taller, add this to the Addition CSS area in the Customizer:

.widget-title, #comments-title, #reply-title, .related-posts .related-main-title, .main .page-title, #nav-below em, .lp-text .lp-text-title, .lp-boxes-animated .lp-box-title {
    background-size: 100% 100%;
}

This will make the background as tall as its content.

The code you provided does not make any changes. This is the code specifically I am referring to that I would like to add space around the text:

#colophon h2.widget-title {
background: #4db562;
}

So this background color for the text needs more spacing around the letters. How would I increase that?

Basically, increase the padding around the text

The widgets titles are designed to have accent colors and not background colors (as you can see in the theme preview and the demo) and this makes it a bit more complicated to alter CSS to achieve something that was not part of the theme’s initial design.

Could you show us a link to your site (with the widget background color applied) and we’ll try to give you the necessary CSS.