Merriam-Webster defines recuse as "To disqualify (oneself) as judge in a particular case; broadly : to remove (oneself) from participation to avoid a conflict of interest." (According to Vox, "recuse" was the most-searched word on Merriam Webster's website on Thursday.)
What this actually means in practice is that if there are any investigations into Trump's campaign, Sessions, the top law enforcement officer in the country, will decline to take part in them. In that case, any Justice Department investigation would be run by the deputy attorney general. Right now Dana Boente is acting in the position, the New York Times reports, but a Senate hearing is scheduled for next week on the nomination of Rod Rosenstein to become deputy attorney general. Since investigations into the Trump campaign will now become his purview if he's confirmed, you can bet questions about Russia, the President and Sessions' recusal will come up in his hearings.
Sessions' announcement came amid questions over his contact with the Russian ambassador in 2016. Both a member of the Senate Armed Services Committee and a Trump campaign surrogate, the Washington Post reported Wednesday that Sessions had met twice with Sergey Kislyak last year, after saying in his confirmation hearing, "[I] did not have communications with the Russians." Sessions maintains he did not discuss the presidential campaign with Kislyak and did nothing wrong, but that he decided to recuse himself anyway. "I should not be involved in investigating a campaign I had a role in," he said Thursday.
The White House defended Sessions. Trump called him "an honest man" Thursday night and said, "This is a total witch hunt!"