Bee traits and their possible values (taken from this link, this forum post, and this page on the Forestry wiki)
Species: determines products generated and base temperature/humidity levels (which are unchangeable), too many to list
Speed: Slowest, slower, slow, normal, fast, faster, fastest (requires Thaumic Bees/Gendustry to obtain)
Lifespan: Shortest, shorter, short, shortened, normal, elongated, long, longer, longest (requires ExtraBees to obtain)
Fertility: number of drone offspring that will be produced when the queen dies, between 1 and 4
Area: Area (XxYxZ) in which the bee will search for its flower and produce any effects, listed in the beealyzer, largest in vanilla forestry is 11x8x11 (ender bee), with Thaumic Bees and ExtraBees 15x13x15
Flower: what block type the bee requires to be within its area in order to produce anything, self-explanatory with the caveat that the 'nether' flower is netherwart.
Temperature tolerance: Levels up/down from the bee's natural temperature range that the bee will still operate in, best is both 3 with Thaumic Bees and Gendustry, both 2 without
Temprature levels are: Icy, Cold, Normal, Warm, Hot, Hellish (the Nether)
Humidity tolerance: functions in the same way as temperature tolerance but for humidity, best is both 3 with Gendustry(equals both 2), both 2 with Thaumic Bees, or both 1 with Forestry
Humidity levels are: Arid, Normal, Damp
Nocturnal: will function at night, yes/no
Flyer: will function when raining, yes/no
Cave dweller: will function without housing having line of sight to sky, yes/no
Effect: Too many to list, the negative ones are usually obvious, but be aware of the ender bee effect that causes lots of damage to the player. Wearing a full apiarist suit will negate all bee effects for the wearer.
Pollination: speed at which bees will cause different tree types to cross-pollinate and also generate additional flowers around hive, Slowest, Slower, Slow, Average, Fast, Faster, Fastest, Maximum (ExtraBees)
Best Answer
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:![Screen shot of a database](https://i.stack.imgur.com/gPSsx.jpg)
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.