They need to get a "stake" in order to make a claim on a piece of land. George and Lennie have a dream to make a claim on a piece of land and make their own small farm. That is what they keep talking about and what means so much to them.
George and Lennie need to build a stake (this means that they want to save money) so that they can buy their own plot of land and have their very own ranch that they can work together. Right now they are traveling together working for other people on their ranches. Lennie is so excited about making their stake because George has promised that one feature of their very own ranch will be a place where Lennie can breed rabbits. He loves soft cuddly things. This is also a good way for George to control Lennie because he reminds him that he has to behave in order to get his rabbits. If Lennie continues to do bad things George tells him he won't get to have his rabbits. This also foreshadows the last scene in the story when Lennie realizes what George has to do to him.
Although we don't get full details about what happened prior to our meeting the characters, we do know that Lennie killed some rabbits before by squeezing them too hard because he doesn't know his own strength.