The "Nunes Memo" is a 4-page document based on Republican congressman Devin Nunes' investigation that alleges that top FBI officials acted illegally to gain FISA warrants to conduct surveillance on the Donald Trump campaign. It is unclear what it says because it has not been released, supposedly because it reveals classified information about sources and methods that the FBI uses that might put those sources in danger or at least render them useless.
Some Republicans (not all) allege that it is "bigger than Watergate" and will bring the FBI down, resulting in prison for several top officials. Others think that is way overblown. It possibly alleges that the FBI unethically (or illegally) used a source who was also on the Hillary Clinton campaign.
What is likely (and this is just my opinion) is that the FBI got a warrant to conduct surveillance on a Trump campaign official (Paul Manafort, Carter Page, or Michael Flynn), as plenty of them were engaged in questionable business activity with high-level Russian officials, and that this led to something else being found. Ultimately, we will not know until the memos get released, which he can do himself (although it may be a bit risky to go around customary channels) or get the President to do. At the moment of writing, he has not even shown it to the Justice Department, so who knows.
It is worth pointing out that, regardless of the potential veracity of its claims, this is entirely a partisan document. It was created in the House Intelligence Committee without input or consultation with the Democratic members of the committee, so the discussion of it once released is likely to be highly partisan.
Nunes, a former Trump campaign advisor, you might remember, was the person behind the claim that Obama "wiretapped" the Trump campaign, so this is likely an extension of that.