6E would be a “6 Excellent” horse in terms of Breed Standards.   Every player can see a color overview of breed standards ABOVE the horses picture through the colored bar.    For example the following horse would be a 3E 3G horse (3 excellent / 3 good) because the bar above the horse when split into 6 sections has 3 Dark Green (Excellent) and 3 Light Green (Good).    You can also find horses with Yellow (Fair) or Red (Poor) sections of the bar.   

If you own the horse in question, you can go onto the horses page and select the 3rd tab over (pictured below) and scroll all the way to the bottom where it says “Breed Standards” to see the exact numbers.  The only player who can see the numbers themselves is the player who actively owns the horse.   Breed Standard numbers are not publicly posted, they are meant to be found out by players if they so choose.   However in theory you could get the numbers from other players in private.   A lot of us use something like Excel or Google Sheets to document enough horse BS numbers to figure out the BS Number Range for Excellent Numbers.
 

Breed Standards are used for Halter Shows and Discipline Shows scoring / placing.   Having more Green / Dark Green stats can help you sell a horse easier, but there are some players who seek out all red stat horses.   

If you want to find out BS numbers on your own or just see a BS overview here is the wiki link: [Breed Standards]

If you have anymore questions feel free to ask away :)   I will try to check back if more questions pop up and someone else isn't around to answer - or if you have discord you could always ask in the discord server

As for TB - TB stands for Training Boost  (link goes to wiki page for TB calculations)

TB helps a horse gain more PS from each time it is trained.   MOST players will recommend waiting to breed horses until both parents are level 50+ so the foals have a minimum of a 10 TB to help them gain PS (performance stats) quicker.   It is important to note that when breeding horses, a foals full TB will not be achieved unless they fully finish Foal Training 

Wild Horses can be found with a range of lower TBs usually between 1-5, while Foundation Store horses have a TB of 0.   

Player Bred horses and foals with higher TB usually have an easier time being sold vs their lower to none TB counterparts.   It all comes down to the players buying horses at the end of the day, but buying a horse or foal with a higher TB means it will have an easier time gaining PS for disciplines :)

– And at the end it can all help to upping the worth of a horse, but there are A LOT of factors that can play in a horses worth, and everyone plays differently with different goals --