Mindfulness or being mindful is being aware of your present moment. You are not judging, reflecting or thinking. -- Mindfulness.com
Boy am I glad I never took that advice. The last time I decided to disregard the future, let me tell you, whatever transpired next is too embarrassing to print. Consequences happen in the future. You gotta think about them. Mistakes have happened in the past. You better learn from them.
So what gives? Are you supposed to be mindful at all times except when you're, you know, in the real world, doing real-world things, and thinking real-world thoughts?
No. "Caught up" in the first quote refers to the distracted state of mind. Recall from another post that it is not the contents of awareness that define the distracted mind, but the quality of awareness. The second quote says you should not be "thinking." For this to be correct they must not be talking about merely having thoughts but the state we're in for the overwhelming majority of time we typically have thoughts.
To really understand what this state is like, you're going to have to catch yourself in the act of being mindless. The bad news is, the mindless state is not exactly fertile ground for noticing... well... anything. The good news is, you're going to have lots of opportunities in which you're mindless :). But to give you some sense of what to watch for, let me give you examples of thoughts I had within minutes of waking up:
* Crap, I have to give this presentation on Monday, and I don't have all the pieces just right. There's so much to do at work today. I'll have to get this map data... but wait, don't we have a lunch outing? Man, my job is great. But boy, wouldn't it be better if I were working in a fulfilling field? Ooh I should be a wedding dancer. Oh yeah I have a wedding to attend later today...
* Oh man, I really wasted last weekend. I was planning to write on my blog, and I didn't even clean my apartment. Oh but Sunday was fun. That hike was great, remember that boulder we couldn't move? I wonder if the weather is going to be as nice this weekend... hey what's San Francisco like in May?
The future events are tinged with a certain sense of angst born of uncertainty, and the past ones with a mild sense of regret and a yearning to improve so that things start going better. Actually, life is pretty much perfect except for [some stuff that already happened and thus doesn't matter] and [some stuff that hasn't even happened yet and thus doesn't matter]. If only it weren't for all that stuff...
No. It's not the mere fact that this happened or that will happen that are preventing life from being epic and boundlessly free. It's that you're letting these thoughts whisk you away. Make no mistake, they are parasites. These narratives have the power to suck mindfulness out of you, and replace it with a vague sense of "oh no" and "if only." Worse, these emotions have a sense of urgency that will convince you that they need your attention, now. You don't have time to meditate, because by god, you have real life to worry about.
At this point you may be thinking "Well, duh... I shouldn't waste time on regret or fantasy. Tell me something I don't know." I am telling you something you don't know. I'm telling myself something I don't know. In a few seconds you'll be back at it, with those same thoughts whispering gently in your ear that no, this thought is different. This one is important. This is about your career!
It's like a guy in a clown suit keeps driving up in a windowless white van and offering you a lollipop, and every time, you fall for it. And if you're thinking "no, not me!" well, nice to meet you, Buddha.
Think about how you'd feel if you won $100 million right now. Go ahead, feel it. Pretty damn happy, right? But that's weird, because you haven't bought anything yet, and that's what the money does for you, right? Okay let's solve that: you just bought a tropical island with your money. WOO-HA! Think of all the sweet time you'll spend there! Happy again. But huh, you're happy without being there yet, and being there is what you're supposed to be happy about. So then you actually go there, and the plumbing is not quite perfect, and there are a few more mosquitoes than you'd like... In fact, the happiness you felt by winning the money or buying the island probably far exceeds the "joy" you'll experience for 99.5% of the time you're on the island, save for maybe your arrival, when you're thinking "boy, this is gonna be great..."
Unless you're really good at nondistractedness, most of the happiness money will buy you is of the form "this is going to be great" or maybe "man, I'm so cool," which have very limited novelty compared with the ongoing blossoming of actual experience. Even worse (though not much worse, incredibly enough), garbage day comes a lot more often than winning-lottery day.
Anyway, by now you get the point: being distracted is no way to live. But if you're like most people, knowing that won't be enough to convince you to try another way. In fact, even if you've savored the acute, exquisite sense of freedom that nondistraction brings, what you remember of it now is but a caricatured shadow, so even that won't budge you. "And besides," you think, "feeling free... big deal." When you return to the settled presence and purpose of that state, then you'll be in a position to judge which path you really want.
And if you're thinking "gosh, he's right, I really should meditate..." and don't act on it, boy howdy you are doing it wrong. Re-read this post if you have to, or read a better author, but damn, stop futzing around.