Like many speeches, Churchill's is named for a memorable phrase he utters during the speech. Since most speeches aren't given formal titles by the author, the famous ones are known either by something descriptive ("The Gettysburg Address") or by some sentence that really jumps out ("I Have a Dream").

In this one, the title comes from the following line:

I would say to the House, as I said to those who have joined this government: "I have nothing to offer but blood, toil, tears, and sweat" (20)

He's been discussing the wartime transition to his new administration, which has been a bit more rushed and has had a "lack of ceremony" (19) compared to other government transitions.

Churchill wants his audience to know that he's prepared to devote himself 110% to the difficult fight ahead. At a moment where things had changed really quickly for the government, with war imminent, the new prime minister wanted his now-subordinates to know that he was willing to pour his whole self into solving the crisis. Maybe he didn't have a magic wand to fix things, but he was there to work as hard as anyone else in that room.

Plus, if the boss is going to put in all those bodily fluids, the rest of them have to kind of step up their game, dontchathink?