It's really an art to present a graph or a plot and explain it.
When I was a new PhD student I was very impressed (actually slightly intimidated) by how a professor could glance at a plot and immediately have comments or questions. Even complicated graphs seemed transparent to them in a way that I did not understand. This made me feel slow and even slightly stupid, especially if I had made the plot and could not explain the features. Sometimes I was not even sure exactly what data I had put in the plot, since I was still struggling with the tools (if you are in the game yourself: I used Fortran and PAW, and when I started I had only very superficial knowledge of programming).
This made me believe that other scientists, and also other students, would probably understand everything if I only showed a graph. The first times I went to collaboration meetings I would show plots and tables and equations and just assume that since I, who was a beginner, could make these they would surely be self-explaining to the more experienced people in the audience.
But they are not. Will the audience remember the definition you showed three slides ago? Will they know how the trigger works that you are talking about? What points could be easily misunderstood because of your special terminology (like using the words "cut" and "variable" as if they were synonymous)?
I learned a lot since then, and among other things I have some experience with interpreting graphs and data plots. It's not as difficult anymore, which should perhaps not be a surprise. This is a skill that just developed with exposure to lots of ways to present data, nothing that I consciously learned.
At the same time I gained some insight into exactly how much you need to explain, and in what order, and how much of the details of your own little special research corner is completely unknown also to people inside the same collaboration. I don't think I really mastered it yet of course, although I'm much better at it.
What I have learned is that clear communication always makes life easier, but also that clear communication takes some effort. You have to understand enough about your audience to be able to see your own plots with their eyes. And while a picture might say more than a thousand words, it might be worth spending a few sentences on explaining what the important features are and give the others time to take a good look at it. If you just flash a plot for a few seconds you will probably leave the listeners more confused than they were before. (Maybe this should be obvious, but if you have been to some conferences you have seen how it's sometimes done.)