Loosely rephrased, "due diligence" means something like "necessary attention". Strictly speaking, "due diligence" should be used to mean the attention and effort necessary to complete the task correctly. For instance, if you drive with your eyes closed, you are driving without due diligence. Of course, with the way language evolves, this usage has become rare.
Colloquially speaking, it is used to mean the recommended research in advance of a decision - e.g. if you bought a house without checking to see if it was structurally sound, and the house then collapsed, a person might (and certainly a lawyer would) say you failed to do your due diligence before buying it. Checking the build quality is an advisable action to take before buying a house, and therefore many people would consider it a part of the house-buying due diligence. Some might not.
At any rate, it is now, in the business world especially, little more then a buzzword. To do your due diligence is now usually used simply to mean checking off every activity you need to complete before making a decision, so that you are not legally liable if your choice comes back to bite you. e.g. consulting the marketing and legal department before changing your brand name.
To summarize: "due diligence" = "ass covering"