It is an overflow with what appears to be a reverse flow under gravel system. The water goes into the overflow, passing over some batting or something, through some bio media and is pumped to the tank through the tubing. It would appear it was meant to be used with gravel, although it could possibly be used with sand, depending on the flow rate.
The way to set up the overflow would be to place bio material on top of the eggcrate (you could use plastic pot scrubbies from the dollar store, filling the space) and a fine filter material, such as square of quilt batting on the top to trap solid materials before they get to the bio. The batting should fit snuggly so that no crud gets to the bio material. The batting can be removed and discarded when it gets dirty. It should work well, especially if you are using gravel.
If sand was used, there would probably be constant movement where the water exits the tubing. This may or may not be an issue depending on the flow, although it might be an issue for plants.
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