In the solo and 2-player adventure, in order to lower the gates so you can move on, you must destroy the 2 Marks of Set on the ledge downstream on the left.
In the single-player game, move past the Marks and step on the pressure pad in the left corner to raise a pair of wooden ledges on the other side of the stream so you can jump across.
Turn the crank as far as it will go to raise a mirror from the floor.
Then, before the crank winds all the way back and the mirror retracts, jump back across the stream, stand behind the Mark on the left and direct a beam of light through the Mark so the beam bounces off the mirror and hits the second Mark. When both Marks have been destroyed, the gates open so you can exit.
In 2-player co-op, the mirror rotates rather than rising out of the floor. Have Lara jump from the raised block in the water to the ledge on the right side of the stream (red arrow). She can then rotate the mirror so it faces the low wall between the two Marks. Isis or Horus can then shine a beam to destroy the marks just as in the single-player puzzle. The gates then open so you can exit. The pressure pad and grapple ring are not necessary.
NOTE: It seems like the block in the stream was a mistake. Should the developers decide to remove it at some point in the future, you'll need the ring and pressure pad to solve the puzzle. If Lara stands on the left side of the stream and grapples the ring, Isis or Horus can tightrope walk across and step on the pressure pad to raise a wooden ledge. Now Lara can come over to the left side to work the mirror, while Isis/Horus goes back to the right side to shine the beam.
I'm not sure how the 3-player co-op puzzle works. If you have played it, please . In the 4-player version, shown here, there are no mirror and Marks, just several grapple rings and a pressure pad separated by gates. Start by having everyone jump from the block in the stream to the right bank (arrow). Then one of the archaeologists can grapple the ring on the left bank so the other characters can cross. Then have the other archaeologist grapple the ring near the pressure pad so the remaining 2 characters can cross.
When either of them steps on the pressure pad, all of the gates open.
NOTE: Again, the block in the stream seems like a mistake. Should the developers decide to remove it, there's another ring on the right side of the stream, closer to the start, that will allow you to get your characters across.
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