When we use drugs, we are intending to wipe out the bacteria (if it is an antibiotic) that lives within us. If we don't fully use the medication in the correct and specific amount of time, we can create superbugs.
Superbugs are the bacteria that survive after using a treatment. This is extremely dangerous, as once it survives the medication, it now has the genetic material to pass on to successive generations of bacteria. That means that as these superbug bacteria are reproducing, they are giving birth to drug-resistant bacteria, rendering the previous treatment useless.
Taking this into context of the problem:
Multi-drug resistant TB could have risen from people not taking the medication for the specified amount of time, allowing TB superbugs to form and produce offspring.