An individual may feel better before completing a full course of antibiotics, however, this does not mean that all of the bacteria in the body have been destroyed.
If low levels of bacteria remain in the body and antibiotics are stopped then the remaining bacteria could reproduce.
Bacteria that are more resistant to the antibiotic tend to survive longer, therefore the resistant population survives and will reproduce.
The patient is likely to then get ill again as the bacteria keep reproducing and can then be resistant to standard antibiotics.