Per the comments, the quote is from Robert Burton (1577-1640), so we're dealing with almost medieval imagery here.
Although the first steam engines appeared around the time Burton was born, they were crude affairs, and not widely adopted in his lifetime - and Burton being an Oxford classicist, he probably didn't know much about them anyway. Dogs really were sometimes used in treadmills to provide motive power for drawing water from a well, for example (horses, donkeys, and oxen would be used where more power was needed). Obviously the dog never actually gets anywhere; he walks because he'd probably be whipped if he didn't.
The usage bird in a cage still exists, but Burton's sense misses its target on the modern ear, since we now associate this with unnatural confinement. He was alluding to the fact that the caged bird flutters around, but again doesn't get anywhere for all his efforts.
Squirrels in a very chain is a misquote (the word "very", which shouldn't be there, makes no sense anyway). It's a pretty obscure image, but I think back in Burton's day squirrels were sometimes kept as "pets" - on light chains, for the owner's amusement in watching the poor creature scamper around. Again, with no hope of getting anywhere, or actually escaping.
Today, most people would understand all these images are examples of cruel entrapment, but Burton simply presents them as situations where the animal keeps moving because it's in its nature to move. He's thus comparing this to the constant mental and physical exertions of "ambitious" men (not a pejorative term to him). He means men of great ability and vision, who will advance humanity by their tireless efforts, make those efforts because it's in their nature to do so.
The second quote has no connection at all to the first. It's from Blaine Lee Pardoe (1946-2009), a writer of science fiction, and business management books. Doubtless the quote is from the latter - it's just a standard "how to be successful and get rich" aphorism, meaning that if you approach life with the right attitude (i.e. - the one his business management book is going to teach you) then you can use any situation as a lesson, from which you'll learn how to become more powerful and successful. By implication, people who don't buy his book and follow his advice will be unable to do this, and will learn nothing from life except that they are powerless "losers".
Taken in conjunction in a complimentary context, OP is being praised for having an active, enquiring mind, with the expectation that he will use this to become successful, wise, and powerful.