They teach you mindfulness as a way to combat the paralysis that comes with depression and anxiety. Based on eons-old religious practices of yoga and meditation, mindfulness is the secular version that comes with DBT and I learned about it in group therapy.
Mindfulness means putting yourself in the present moment, and it's not as easy as it sounds. First of all, your body reacts to both depression and anxiety, mostly by clenching up. The going theory is that the same "fight or flight" reaction that we're all wired to experience when danger is afoot (say, a tiger) happens when we have the bad thoughts associated with anxiety. That means tensed and ready to run. Imagine being tensed and ready to run from tigers all the time. That's anxiety.
Mindfulness means relax your body. Do this any way you can, I have gotten to the point where I can close my eyes and scan my body from head to toe relaxing each part of me as I go. You need to breathe, deeply in and out, and counting can really help, slow counting of the breaths. It's a lot like meditation or yoga. Then you have to use a "stop" technique on any negative thoughts that come in, but you can't fight the thoughts, you have to regard them and then let them go right past. They call it "teflon mind." There's the thought, you say. Have no opinion about it. Let it pass. Move on.
Mindfulness is breathing in and out, relaxed, and thinking only of right now. Listen to what you can hear, look at what you can see, feel what you can feel, and bring yourself only to right now. If you find your thoughts wandering or rumination starts up, begin again. Be in the moment, and as you go along you can tell yourself a mantra. I used to say "mindful" until someone on Facebook told me "be here now." Now I say "Be here now." I count the breaths and relax my body and say "be here now" and when I get lost, I come back to the breaths.