This first picture is from the Beealyzer. The picture is obviously supposed to represent the possible mutations, but I can barely see the picture let alone figure out what it means.
This second picture is from the Apiarist's Chest. I'm assuming that like the first picture, it has something to do with mutations, but again, the picture is entirely too small and not detailed enough.
How can I see and\or understand what these pictures are of, or what they mean?
The possible mutations screen is just that, the possible mutations. It is to let you know how many different combinations are possible with that bee. In case of the first screen shot above the been you have analyzed has 6 possible mutations (change into another bee) of which you have found one.
The Apiarist Chest shows this same information but only the resultant bee instead of what the combination bee and that bee will turn into.
If you have the addon mod 'Extra Bees' then you will have access to a tool that can give you a better run down of the information. It is called the Apiarist Database and is made in a carpenter. It will give you an interface like the following screenshot: 
In the shot above you can see that I have a Noble bee selected and show that one of its found mutations is to a Majestic bee with another found one below that (Imperial) then several unknown mutations. The ? on the bees mean I have never seen that bee type before, the bees that are just outlines means I have found the bee but I have not made the mutation as of yet (Those are the bees in the second row there and when there is only one of them it is usually the selected bee but if you look at the last row you will see I have two bees that should be able to breed to produce a mutation, I just have not gotten it yet.)
Hope this helps.
