Quite frankly, this is a trick question. There are at LEAST three interpretations of the end of Of Mice and Men by Steinbeck! Therefore, it is not fair to say what is "the" interpretation, but might be more fair to ask what the "usual" interpretation is. Here, I will discuss the three possibilities so that you can decide for yourself.
First, the most common interpretation is that "the end" of Of Mice and Men happened because of George's loyalty to Lennie as a friend. Carlson and Curley are after Lennie (and this time George can't save Lennie). Why? Because Lennie has accidentally killed Curley's wife. There is no escape from this crime, and it doesn't matter that Lennie isn't mentally able to comprehend his actions. Lennie runs to the river first and, where at the beginning of the novel he gulps the water, now he just sits quietly and hardly takes a drink. George isn't far behind Lennie, but George hasn't forgotten to pick up a gun first. This secures George's final gift to Lennie: death in happiness and innocence instead of death in anger and confusion. George and Lennie, of course, have planned their dream of owning a farm through the whole book. George asks Lennie to describe their dream one more time. Lennie happily does so, while George lifts the gun (with his hands shaking) and shoots Lennie in the back of his head, killing him instantly. In this interpretation, it is love that causes George to pull the trigger. George would rather be the one taking Lennie's life as he muses on his happiness. The alternative was full of hatred and anger and confusion and fear. Such actions are the actions of a true and loyal friend, the friend spoken of here:
A guy needs somebody―to be near him. A guy goes nuts if he ain't got nobody. Don't make no difference who the guy is, long's he's with you. I tell ya, I tell ya a guy gets too lonely an' he gets sick.
Now, other interpretations suggest that George is truly getting Lennie "out of the way" in order to achieve the dream of owning his own farm. Some scholars say that George can only achieve "happiness" without Lennie. Some scholars say that George can only have a farm alone, while others say that George really plans to create this farm with someone else. I can't say these interpretations are completely unfounded. Look at what Slim says at the end (after George kills Lennie and George looks crestfallen):
Slim twitched George’s elbow. "Come on, George. Me an’ you’ll go an’ get a drink."
Some scholars say that this is Steinbeck's way of showing that Slim can take Lennie's place and, further, as the "God-like figure" of the book, is actually a BETTER companion than Lennie. I'm not quite so sure that statement by Slim is enough for me to believe that, but I do see the point.
As some scholars admit, then, the ending is meant to be ambiguous. It is not a happy ending by any means, but one where George could either be hopeful or hopeless depending on the interpretation you choose from above.