Science cannot give up its extremely specific terms. They're simply required for a succesful communication inside the perimeters of univocity and precision. What you suggest would require for all or most of the concepts on that text to be substituted by its definition. And that's not practical.
However, not everything is lost. Because what you need to understand that tricky word is but a quick wiki search away. In fact, I think the wikipedia is the best gateway into any new topic for a layman - scientific or not. The English wikipedia is very accurate and has a lot of content that can go quite in depth while giving you instant access to the explanation of this or that concept you don't seem to be able to grasp right away.
What's the key to get the general public to learn about science? Their own natural curiosity. And I think nowadays Youtube is doing an amazing job at spurring it. You can watch short videos with a lot of info crammed into them that will get your brain started on certain topic. Then you only need to get that person used to looking for the answers to the questions that they'll eventually get and that's it. Now we have a better educated citizen. They even found it enterteining, which means that they'll come back next week for a new video, and then start on that new topic and... The ball just keeps rolling.
Of course, this isn't enough to get a person to the highest level of any science. But I think it fulfills what you were asking for.
P.S: I'm going to post a few links to channels I think are good examples of what I'm talking about. Feel free to browse them, all are worth your time.
https://www.youtube.com/user/destinws2
https://www.youtube.com/user/CGPGrey
https://www.youtube.com/user/scishow
https://www.youtube.com/user/crashcourse
P.P.S: I hope my sleep deprived brain hasn't made an ass out of me in this post. I really wanted to contribute ^^