I'm really sorry if this isn't tech-y enough for this forum. I wasn't sure where else this would be appropriate.
It's tech related and technical in nature (as opposed to being geared for a general audience); you're in the right subforum.
They're really powerful tools for understanding and tinkering with web pages, and they're especially useful for figuring out what changes you need to make to the pages as they're delivered by the server. You can, for example, try a variety of CSS style rules on a specific class until the page in your browser appears as you want it to appear, then change the server side CSS to match your newly made rules.
Keep in mind that DOM editor tinkerings are temporary; unless otherwise saved, they'll be wiped on your end with the next page load, and they (again, unless saved on the server side) will not affect the web page as viewed by other browsers at all.