Meditation is a practice that allows us to realize the absolute freedom of our own mind. It allows us to sit with ourselves and be with ourselves no matter what thoughts or emotions are coming up. Without meditation, we don't typically do this.
The mind is filled with all sorts of thoughts and concepts. It's constantly fielding all the input that comes in from our environment, and from our inner world.
Meditation is not about stopping our thoughts. Meditation is not about getting rid of feeling and emotions. It's about not getting all tangled up with them.
An Analogy: Your Mind is a Busy Street
Take a moment and imagine yourself sitting on the side of a very busy street. Cars are whizzing by, each one holding all the thoughts and feelings we experience throughout the day.
The point of meditation is to simply watch the cars go by.
We can get better at this through practice and guided meditation for anxiety, but that's not what we typically do. Most of the time we're chasing after them or trying to stop them. All this running around out in the middle of the street trying to play "thought cop" only makes things more chaotic. In fact, we're apt to get hurt and probably hurt others in the process.
Meditation gives us a new perspective and trains us to change the way we interact with all those passing cars (our thoughts and feelings). We learn how to look at them from a bird's eye view. This lends more perspective to things.
Of course, we'll forget from time to time what we're training our minds to do. We'll jump into the traffic again and start playing traffic cop. But as soon as we do this, all we need to do is remember the practice, step to the side of the road and simply relax. There's nothing to do but watch all those cars passing by, once again.