Whenever you opt for a new theme, you’re going to have to do a fair amount of customization to get everything just right for your site. By the time you get to your third or fourth theme, you’ll probably begin to grow a little weary of reinventing the wheel with each new design.

Fortunately, savvy users like you can solve this problem by creating a user-defined functions file that will work with any WordPress theme. Pearsonified has shared How You Can Use WordPress Functions to Run a Smarter Blog by placing all of your common, customized design elements within functions that reside in a separate, non-theme file. This serves a twofold purpose:

First, because your common design tweaks are isolated in a non-theme file, you won’t risk overwriting them whenever you change or upgrade your theme.

Second, using a separate functions file creates a much more organized and less intimidating environment for customizing your theme. You can add and subtract HTML from your user-defined functions file without fear of “breaking” your theme, simply because you aren’t trying to edit the theme files directly.

Source: How You Can Use WordPress Functions to Run a Smarter Blog