At the top of the steps, near where you entered this area is a rope-wrapped lever, a shallow pool, and a jaguar-head handle. On the level below are 2 columns with grooves around their bases. Both have rope coils, and one has handle that allows you to rotate it. The idea is to line up the grooves so the oil can flow down from the pool at the top of the stairs, all the way to the wooden barrier beyond the columns. Then you can ignite the oil to destroy the barrier.
To do this, start by standing near the shorter column.
Shoot a rope arrow into the taller one...
...to tether the two together.
Now grab the handle sticking out of the taller column and rotate the column 180 degrees (i.e., two notches in either direction). Thanks to the rope tether, the smaller column also rotates.
One of the curving grooves at the base of the short column should now connect the center groove between the two columns and the groove leading to the wooden barrier.
Cut the rope.
Now grab the handle again and turn the taller column 90 degrees (one notch) counterclockwise...
...creating an unbroken channel from the pool at the top of the stairs all the way to the wooden barrier.
Return to the upper level...
...and use a rope arrow to pull the lever that opens the vat of oil.
If you've lined everything up correctly, the oil should flow into the pool and down the stairs...
...along the grooves in the floor, all the way to the wooden barrier. (If not, you can manipulate the columns further or reload the checkpoint and try again.)
Once you've filled the channel from the pool to the barrier, pull the jaguar-head handle to ignite the oil.
The flame should then travel along the channel to the barrier, destroying it so you can continue.