"Old longings nomadic leap,
Chafing at custom's chain;
Again from its brumal sleep
Wakens the ferine strain."
The epigraph is taken from "Atavism," a poem by John Myers O’Hara. The fancy-pants word "atavism" refers to a reversion to older forms—basically, these four lines address ancestry, instincts, and history.
This, of course, isn’t surprising; these are pretty much the major themes in The Call of the Wild, and epigraphs tend to be relevant to the work they precede. Good job, epigraphs!
Now that we’ve talked about the epigraph generally, we can jump into this excerpt and dissect it like so many Biology 101 worms, starting with "Old longings nomadic leap." The first thing that’s confusing about this line is that the noun and adjective are out of order. Think of it as "old nomadic longings are leaping." (It doesn’t sound nearly as good, which is why O’Hara didn’t write it that way.) "Nomadic" refers to nomads, which are traveling people with no permanent home. Basically, if you’re stuck in one place, your old nomadic longings are going to flare up and send you packing for an "elsewhere."
Yet these nomadic longings do more than leap. They also chafe, and more specifically, chafe at "custom’s chain." No, not airport customs, but customs as in traditions. If you can see traditions as a chain that holds you back, then this poem did its job. The longing to travel is at odds with the tradition of staying in one place, which is why the "longing" starts to "chafe" the "chain."
In the third line, we’ve got "Brumal," which really means "winter-y." This bit is talking about winter-y sleep, which makes us think of hibernation, which makes us think of wild creatures like bears. More than just talk about sleep, it’s talking about waking from that sleep, which fits with the whole, "I really want to get out of this place" nature of the first two lines.
Last, we have the word, "ferine," which means "feral," and is a fancy word for "wild" or "untamed." "Strain" refers to a kind, type, or variety (think "strain" of bacteria). This line finally brings us home. To work backwards, "the ferine strain" is the wild type of creature, that is finished with sleeping during the winter, tired of playing by the rules, and ready to get out of this place already.