HIV or human immunodeficiency virus infects the cells of immune system, causing them to produce more copies of the virus and then eventually die. When too many immune cells of your body die and our immune system is unable to fight off diseases, then we are said to have AIDS or Acquired immunodeficiency syndrome.
Now, coming back to the question. It is hard to cure HIV or AIDS because HIV has the ability to mutate extremely quickly. Hence, a drug which is somewhat effective on a patient suffering from HIV or AIDS, might not work on another patient because of the mutated HIV. Now, there are certain antiretroviral drugs that prevent the cells from producing new copies of HIV, thus controlling the HIV levels in our body.
But, it is hard to completely eradicate HIV because the virus integrates its DNA into our cell’s DNA. Hence, if we stop taking the drugs, the DNA of the virus can again cause the cell to produce copies of the virus and thus, we are unable to control the level of HIV infected cells in our body.