"Work cards" were issued by the WPA (Works Projects Administration) in an unprecedented effort by the Roosevelt administration to get money into the pockets of the thousands of men who were unemployed during the Great Depression.
The government would repay employers who hired men who had signed up for this sort of relief; essentially, the employer got free, or nearly free, labor in exchange for hiring men who were out of work.
To be eligible for hire, a man had to sign up at the WPA. He was given an identification card and a "work card." The identification card must be shown to the potential employer, and the work card surrendered for the duration of his employment. The employer could then submit the card information to the WPA agency for repayment.
This is why Lennie goes into something of a brief panic when he thinks he's lost his ticket:
"Geroge, I ain't got mine. I musta lost it." He looked down at the ground in despair.
"You never had none, you crazy bastard. I got both of 'em here. Think I'd let you carry your own work card?"
Geroge had good reason to be wary. Without the cards, the pair certainly would not get a job.