In this comment from Chapter Four, Nick is making a statement about the nature of the people he has encountered since moving to West Egg. By the "pursued," for instance, we can infer that Nick is talking about Daisy, the object of Gatsby's affection. This, in turn, makes Gatsby the "pursuing." The "busy" is, perhaps, Jordan, Nick's athletic and socialite girlfriend, or Tom Buchanan, the man who splits his time between his wife, Daisy, and his mistress, Myrtle. Finally, the "tired," perhaps, also refers to Daisy Buchanan, who spends much of her day resting at home and drinking with Jordan, and who is already jaded by life, as she admits to Nick in Chapter One.
Nick has, therefore, exposed the truth about the people of West and East Egg. He has realized that, for the most part, they are empty and shallow, concerned only with achieving their own ambitions and serving their own interests. This, perhaps, also accounts for his "heady excitement" at creating this phrase: he has realized that he is nothing like these people and that makes him very happy.
Nick's thoughts reflect the angst of modern life. As he holds the superficial Jordan in his arms, he wonders why any of the pursuit of love, riches, and so-called "happiness" are worth anything at all.
Break this quote down into pieces and it is much more understandable. For example, the "pursued" are Daisy by Gatsby, and Tom by Myrtle. The pursuing are Gatsby, trying to "capture" Daisy, and Myrtle trying to snare Tom.
I would argue that "the busy and the tired" include all of the characters. These traits, again, are indicative of the shallowness of modern life. It seems that no one really wants to play the game of predator and prey, yet no one truly wishes to give up the thrill of the hunt either.
But thrill is temporary, and its promises of pay-off illusory. In the end, the characters lack rest and contentment, a price they have paid for the more temporal benefits of a quick fix (that is, parties, false camaraderies, fleeting fame.)