I have always been puzzled by this - and when I asked Support, they did not know either.
Eventually one of the Moderators explained it to me:
It is a mathematical relation based on the 12 minutes that it takes to train a basic unit in a level one Barracks - so in practice, the number means how many units you can train in 12 minutes, in each level.

You are welcome to share with friends, fellowship and map neighbors!!

Elvenar Platinum Leaf is a public Facebook group with 3900 members, with hundreds of items of Elvenar facts, as well as a growing collection of videos.
You and your fellowship are welcome to join!

I haven't seen a ticket about this at the Elvenar International support team, but that also doesn't matter much. Let's answer the question nonetheless.

The training speed starts at 1 for every player. When you upgrade your Barracks (or build/upgrade certain Ancient Wonders), you can increase the training speed. The higher it is, the faster you can train your units. For easier explaining how it works, let's consider the training speed as a percentage: training speed 1 becomes 100%. If you upgrade your training speed to 2, this would be 200%. Upgrading this speed to e.g. 35, would mean 3500%.

The percentages can become a bit hard to read (especially at higher levels), which is why we display these values as "normal" numbers, rather than percentages. 'Translated' back to normal numbers, you could say that the earlier training speed of 35 means that 'you train units 35x faster than you could when you started.'

Want to go even deeper into this? (optional extra for those who like maths)

OK! Then let's do just that.

Another thing to consider then, is that every unit has a basis training time ('base time'). This can be seen at Barracks level 1 (=100% training speed), and at this level only (if you upgrade the Barracks, the training speed increases). Of course you can calculate it back, if you want. If you then take this 'base time', you can calculate exactly how long it will take you to train a single unit:

base time / training speed = training time

Example:
A unit needs 12 minutes to train with a training speed of 1. This means that 12 minutes is the 'base time'. If you then have a training speed of 4, the time it would take you to train one of these units is:

12 minutes / 4 = 3 minutes

As you can see, when you upgrade your Barracks and increase your training speed, you can significantly reduce the training time needed for 1 unit. Of course you will also need more units when you're advanced, so that also balances out that way.

I haven't seen a ticket about this at the Elvenar International support team, but that also doesn't matter much. Let's answer the question nonetheless.

Thanks!
I incorporated that info into our Tip.
There is a graphic in there too that shows training speed for each level - and how that affects training time for a basic unit!!