If I recall correctly, the Precipiton feature is newer than the manual. The general idea of the feature that that the system drops agents on the surface, which move downhill in the direction of steepest descent to a low point, moving some amount of elevation difference between cells as they do so. The total number of agents per pass is equal to the number of samples on the surface and each agent is dropped at a random location to start. Dropping them randomly prevents a certain class of artifacts that happened with an earlier implementation, but it doesn't guarantee that every point on the surface will be eroded equally.

At every step in an agent's life, it looks at the surrounding cells. How many cells it looks at is determined by connectivity: 4 (the four cardinal directions: up/down, left/right) or 8 (the four cardinal directions plus four diagonals). Of those surrounding cells, it finds the lowest one and adds Delta * (difference in height between current cell and lowest neighbor) to the lower cell. It then moves to the lower cell and repeats the process. This process repeats until the agent is in a pit surrounded by higher cells, until the agent runs off the map, or until it hits its maximum allowed number of steps. How the agent determines the edge of the map is controlled by the Wrap item: "None" means moving over any edge is off the map, "X Only" means that moving off the edge in the horizontal direction wraps around to the other side, "Y only" means that moving off the edge in the vertical direction wraps around to the other side, and finally "Both X and Y" wraps both horizontal and vertical directions. How many steps the agent can take is determined by the Max Length item: a value less than zero means that the system should pick a maximum number of steps, while values greater than zero will only let the agent move that number of steps.

That covers the Basics of the Erosion (Precipiton) Setup dialog. The Multi-Pass section is all about laziness. I became tired of repeatedly opening the dialog to get my desired final effect and I added the Passes feature, which repeats the above process the number of times specified. I'm not sure when the last time that I use the Blend or Noise features; they control the amount of blending between the uneroded and eroded surface for each step and the magnitude of noise to sprinkle on the surface at each step, respectively. If I ever get scripting working, this section will probably become a link to a parameterized script.