Whitey's sudden departure illustrates the itinerant nature of the lifestyle of ranch hands, and the resulting difficulty of developing lasting ties with other people.
The old swamper tells George about Whitey, who was the last one to occupy the bed now assigned to George. When George asks why Whitey left, the swamper replies,
"Why...he...just quit, the way a guy will. Says it was the food. Just wanted to move. Didn't give no other reason but the food. Just says 'gimme my time' one night, the way any guy would".
It is not unusual to ranch hands to just up and leave for no apparent reason. The swamper is a little surprised that George should ask why Whitey left, because it is something so commonplace that the old man hadn't even thought about it. In looking back, the swamper perceives that Whitey's stated reason for leaving - the food - isn't really much of a reason at all, and so he concludes, probably rightly, that when all is said and done, Whitey "just wanted to move". Ranch hands do not very often stay in one place for very long. For Whitey to have left the way he did was not unusual.
Because they do move around so much, the life of a ranch hand is a lonely one; they do not very easily establish close or lasting friendships. This is evident in the swamper's recollections about Whitey. He remembers Whitey's propensity for cleanliness, the way he used to wash so scrupulously and his finickiness about the food. He also recalls his unusual habit of dressing up on Sundays "even when he wasn't going no place". All of these are surfaceful observations, however; although the swamper can describe things Whitey used to do, he knows nothing about what he thought or how he felt about things. He doesn't even really know why Whitey left, nor did he think to inquire (Chapter 2).
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Ranch hands can’t have a prosperous life. They can’t stay clean. When Whitey gets dressed up on Sundays, it is because he is observing church day, the Sabbath, in Christianity. He has nowhere to go, showing that with no church to go to, religion and hope are lost on the men. Most importantly, the fact that his sudden leaving is so common shows that ranch hands are transient, with no stability or chance to make a better life. This is important because it shows contrast with George and Lennie’s plan. It gives the reader a reason to have hope for them.