It sounds like the bucket w/the holes, inside of a hole, is a 'collection point' for water that enters the basement. I'd guess that the water would 'run' towards the buck, perhaps leach into the ground a bit on the way, and eventually make its way into the buck via the holes at various heights in the bucket.
Water, by nature, will find its way to a location of 'least resistance'. THen, once there, it would probably leach 'deeper' into the ground in the bottom of the bucket. I'm assuming that the bucket has holes in the BOTTOM of it as well. And hopefully, the bucket is 'surrounded' by some sort of filtering fabric. It's not enough to surround the bucket w/just gravel, IMO.
If the basement floor is dirt, you have mud when it rains. ANd if whatever water you collect isn't 'filtered' in some way, that mud/dirt will ruin any pumping system you use in the basement.
Have you 'inspected' the roofline AND landscape ALL THE WAY AROUND the house during a rain storm? Don your boot and umbrella and raincoat (watching out for lightening), and do this type of inspection. You may find that you can reduce, perhaps eliminate your water problem, by 'fixing' leaking gutters, hanging gutters where there aren't gutters, grading your landscaping AROUND the foundation/crawl, and extending your downspouts to a MINIMUM of 3' from the foundation. These are very, VERY inexpensive remidies assuming your home is 'lacking' these common fixes.