Biohacking is a term that many people are starting to use for a type of self-improvement. In many ways, the term is a tacit acknowledgment that your perceived failings are not entirely at your command. That you are at odds with the way your body, biologically, wants to operate.
Sleep is probably the most common one. Getting enough sleep is the key to good health and longevity. Most people, everyone will tell you, don't get enough sleep. So there are different biohacking apps designed to help you sleep. There are some that use binaural beats to change your brainwaves to be more receptive to sleep. There's some that wake you up during the ideal part of your sleep cycle to be woken, to feel more rested. There are some that change the hue of the light from your phone or computer to match a diurnal cycle better. There are dozens of apps based around these or other biological functions that aim to help you sleep better and more regularly.
The purpose of the examples is to prove the point. Biohacking is an attempt to use your own body's functions to make it operate more ideally. Imagining your body as a machine that you don't have full control over is useful in this context and somewhat true. You likely learned about involuntary muscle movements and brain functions in school. Biohacking proposes to use the basic functions of your body, things you have no voluntary control over, to help improve your life.
You get into it by using apps, generally. There are other paths, but apps are really accessible to almost everybody who has a smartphone, tablet, or even desktop computer (though some of the functionality you would get from mobile apps is absent in desktops).
You can do lots with biohacking. There are apps that cover training your brain to have better recall. This is useful for most people but particularly useful for people who are getting older. There are studies that suggest that brain exercises can actually delay the onset of dementia and Alzheimer's. Sleep, as already mentioned, can be improved with the use of biohacking. There are apps that handle stress reduction. Stress is a known factor in a lot of physiological diseases; reducing stress is believed to keep people healthier for longer. Many of these apps can help you monitor your own heart rate, which is a factor in stress, and reduce it, though some will need additional hardware to do this. It's worth looking into the variety of ways that biohacking can help you.
To learn more, look into biohacking apps.