Earlier quoted context omitted.
From my understanding, our minds are are not literally filled with things in the real world (for they would not fit) but are instead filled with "thoughts" which "refer" to real things. But my "thought" of peanut butter, for example, might have significantly different "connotations" for me than for someone with an allergy to peanut butter. So what I'm saying is, these "thoughts" and what they "connote" to the individ…
So how would you alter your thought of a real problem if it seems legitimate to worry about it?
The only mechanism by which 'worry' might be useful is if it triggers the problem-solving part of the mind and ultimately leads to actions that solve this problem. In my opinion this mechanism is highly inefficient and in fact often backfires: we focus on the worry instead of thinking about solutions, let alone implementing these solutions.
Meditation, and a mindful approach to life is first of all useful as a debugging mechanism. As you train your ability to direct your thoughts and pause them, you learn to discern what kind of thinking is useful, and what isn't.
So, for example, you might realize that you've been caught up in worry and just the act of being aware of this pointless train of thought might prompt you to sit down and create an action list of how to get out of this situation.
Another benefit is that frequent meditation somehow improves the connection between the thinking mind and the subconscious, as well as the body. I've had moments where meditation helped me suddenly realize a solution to a problem that I couldn't previously solve. And almost every time that I meditate, I will be aware of hunger, or thirst, or some other feeling or physical need that I would otherwise completely neglect.
Now I'm a particular type of person, so these benefits might be more explicit to me, but from what I understand most people will experience these things to some extent.