When someone is diagnosed with a mental illness, there is always the possibility that they will get "better", especially with therapy, coping techniques, even medications and all the other ways that will alleviate the negative symptoms of the mental disorder. Yet, whether they will be "cured", depends on the mental illness. For example, there are some mental illnesses caused by genetics, deformations of the brain, and chemical imbalances: mental illnesses caused by these factors are never going to go away completely, but they can and will get better if an effort is put into it, even in most cases to a point where whoever in question can live a normal and happy life.
Being diagnosed means you are able to get the help you need. Chances are you still had your condition before being diagnosed. Though now that you are, professionals can help you can the correct medication and therapy. If you have been diagnosed, consider it the next step on your journey to achieving a better you.
If by better you mean can it be controlled to a degree then yes. Through Cognitive Behavioral Therapy and a close monitoring of medicines which seek to bring mood stability. Google the specific mental illness you want to find out more about to answer your question on can yours get better with current methods. I only know mine, it does not improve, will not and has specific ends ahead, but it can be slowed. Age is a factor as is exercise, diet and other activities you can engage in. Bottom line take charge of your own treatment and be proactive in your care.