Thanks for the replies. To answer the questions, there is a sump pit with a non-functioning sump pump in it. The pit is full of some debris left-over from when the previous owner did major construction...and there is dirt in the pit. The pit looks like a black plastic container. In three years, there was only one time where there was water in the pit...and it only amounted to dampness, not even enough water for a puddle. Note that the black drain pipe in the floor empties into this sump pit.
Regarding the question about the channel of dirt and the drains, the dirt channel runs around half of the perimeter of the basement floor. The basement is a rectangle with the sump pit in the middle of the front wall. So, half of my front wall from the sump pit to the side wall has a drain buried beneath the concrete but a few inches away from the dirt channel/wall. Then there is a dirt channel and most likely drain along the whole side wall. Finally, there is a dirt channel and I'm assuming a drain along half of the back wall. Thus, half of the perimeter of the basement has this dirt channel, and since I see the black pipe going in to the pit, I'm assuming drains run along this perimeter as well.
But again, I haven't seen any significant water go in the pit. However, one corner of the basement (dirt channel exists in this corner) has signs of water marks on the floor since I moved in. A few times there has been dampness over an area of about 3'x3' on the concrete floor. However, I think this might be due to rain water from the gutter in the corner of the house...I need to route this further away from the house.
Please let me know your thoughts and how I should remove this dirt and replace with gravel. Should I just pull it up with a garden trowel?