The Nunes memo was supposed to be a great move in the Republicans' war against the FBI. I think its release fell flat, for reasons spelled out in several articles which came out after its release, but given the extremely tribal nature of today's American politics, I'm certain-sure that most Republicans found it a real smoking gun (check the comments on that last link!).
I get the importance of any move which could stop the Mueller investigation into the Trump campaign and the Trump administration. Republicans don't want to go down with the captain of their ship, even if that captain himself drilled the holes in the hull.
And for the Mueller investigation to stop, Trump needs to get rid of Deputy Attorney General Rod Rosenstein:
Rosenstein is key to the Russia investigation because he has the power to fire Mueller, after Attorney General Jeff Sessions recused himself from the Russia matter.
But Rosenstein isn't firing Mueller. If Trump could replace him with one of his own stooges, that stooge could then fire Mueller, and Trump believes that he would then be safe from further harassment. The release of the memo had the partial goal of making Rosenstein's firing seem more appropriate.