It's talking about dilution. It means that if there is, for example, an enormous vat of water with a tiny drop of a chemical compound in it, a dog will still be able to smell that chemical. Even if the proportion of water to chemical is a trillion to one ( 1,000,000,000,000 parts water to 1 part chemical compound), the dog will detect it.
The 'going down' part of the sentence means 'as few as' or 'a little as'. Imagine that you're doing a series of tests, comparing the olfactory sensitivity of dogs and humans, gradually reducing and reducing the amount of a substance present. Humans would soon fail to detect the presence of a substance once it was diluted. With dogs, however, you could keep reducing the amount of the substance, down and down, and they would still be able to smell it.
In practical terms, this is why a sniffer dog can identify an infinitesimal trace of cocaine on a person's clothing, for example. A dog can smell a person, and amid all the trillions of other smells on that person (their skin, hair, clothes, soap, detergent, smoke etc), they'll still pick up on the tiniest particles of a drug.