In simple terms: to make Nuclear fuel, natural Uranium must be enriched by separating the different Uranium atoms, with certain parts of the Uranium then being used as fuel for nuclear fission - the process which creates nuclear energy for bombs and power plants - and the leftovers are what we describe as 'Depleted Uranium'. When absorbed by humans and other living creatures, this Depleted Uranium is generally mildly radioactive, but highly toxic.

Here is a slightly more technical description of how DU is produced...

Refinement Of Uranium To Accumulate The U-235 Atom For Energy/Weaponry Uses

Natural Uranium is composed of mainly three types of Uranium atoms (also called isotopes). It is composed of approximately 99.27% Uranium-238 (U-238), 0.72% U-235 and 0.0055% U-234. For nuclear reactor fuel, and for nuclear bombs, it is necessary to have the level of U-235 in the Uranium as high as possible, and the enriched portion - which ultimately ends up as nuclear fuel - usually contains most of the U-235.

DU Is A Waste Product Of Uranium Refinement/Purification

The leftover portion, the Depleted Uranium, mainly consists of U-238, it has less than a third of the natural levels of both U-235 and U-234, and is about 60% as radioactive as natural Uranium, which is significantly less radioactive than the enriched Uranium. It appears that the main problem with DU is not the radioactivity levels - although they may be an issue - rather it is the levels of toxicity, brought about by the addition/production of potent substances during the refinement process. Plutonium is one great example - most of that highly toxic chemical element has been produced by humans, as a byproduct of Nuclear Fission.

Non-Conventional DU Can Be Even More Dangerous

Depleted Uranium can also be a waste product of reprocessed spent nuclear reactor fuel, and this kind can be distinguished by the presence of another Uranium atom, U-236. If reprocessed Uranium is present in DU, it may be considered much more dangerous to humans, with higher levels of radioactivity present, plus the possible inclusion of even more harmful substances, which were produced/used during the secondary nuclear fission process.

Read more about why militarized DU is used extensively by US/UK military forces.
Read more about Human Health Effects associated with exposure to enriched Uranium.