I wouldn't say that mindfulness is "achieved" at all. I would say it's something we practice and strive for in order to live a better life. If you're looking for a more scientific definition, I'm not sure there is one. The study did, however, find quantifiable effects of engaging in mindfulness training, including better performance on attentional control tests.

Mindfulness means being fully aware of the present moment, rather than being caught up in your own thoughts. It's basically the opposite of being on autopilot. Mindfulness training or meditation is simply practicing being aware of the present moment for a length of time (could be an hour, could be 5 minutes, could be a whole day). When meditating, a good anchor to tie you to the present moment is your breath. Be aware of your breath - breathe in, breathe out. There's no need to control the depth or speed, just breathe comfortably, and feel each breath in your lungs, chest and abdomen. Notice your hands, shoulders, legs, feet. Release any tension you're holding. When your mind wanders, notice your thoughts. Accept them, and then gently bring your attention back to your breath. If you feel any emotions, notice and accept them too, then gently bring your attention back to your breath, in and out. Try setting a timer for 30-60 seconds, just to try it out. Then try 5 minutes. If it's going well, try making it a daily habit. You can gradually add more time per session if that feels right for you, or you can keep it short and sweet. There is no wrong way to practice mindfulness. If you are able to redirect your attention from a passing thought back to your breath even one time, you have succeeded. My final tips are that it helps to have a comfortable place to sit, and to set a timer for your preferred amount of time with a nice calming bell or other soothing alarm sound.