In the trailer, the camera pans over a bunch of swirling numbers. These numbers form the silhouette of a man holding a pistol and a knife, and then another man pointing two pistols downward. These are the characters seen in the box art for Black Ops and Black Ops 2.
Throughout the video, we hear lines from the past two games:
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This should help you remember everything.
  The numbers, Mason, what do they mean?
  Everything you know...is wrong.
  Your life will be consumed by absence and loss...
  He doesn't need his own weapons. He's got ours.
  They'll always need men like us
The last line of the trailr, however, sounds brand new: "Our greatest barrier is our own fear, our own doubts. The only thing holding us back is how far we're willing to go."
Then, the number one appears. It splits into two and then into three. We're then told to expect a "World Reveal" on April 29th.
Call of Duty: Black Ops follows covert soldiers working in the Cold War. The sequel was set in 2025 during a new Cold War, with flashbacks to the eighties. Presumably Black Ops 3 will either take place chronologically after BO2.
What remains to be seen, though, is how far into the future they'll go. Will we see another game set in the 2050s, the time period of Call of Duty: Advanced Warfare. The exoskeletons in Advanced Warfare were arguably the biggest change the series has seen in years so maybe Treyarch plans to build on them for BO3. It might feel like a step backward if those exo suit abilities weren't in this year's Call of Duty.
I'm sure we'll find out what the deal is on April 29th, though. We've already gotten the short logo teaser so the next trailer's going to need to be more substantial and actually tell us something about the game.