What are the benefits of meditation in our life?

Hatha Yoga, postures and breathing exercises, and meditation, are each one of the eight limbs of “Raja Yoga” (Royal Yoga) practice.
Yoga is a philosophical system with the goal of peace of mind so substantial it leads to enlightenment.
Hatha Yoga is designed to calm and energize the body so that when one is meditating, one is not distracted by aches and pains, and one does not fall asleep. It also develops self-awareness as one faces the challenges of the postures (asanas) and develops the mental focus needed for the most difficult of them.
Meditation is designed for mastery of the mind so that one can get to the point of meditation (direct experience of consciousness and existence) without the wayward thoughts taking the attention away.

In the West most people come to Yoga through Hatha Yoga, and it’s a good place to start. As you learn more and increase your self-awareness, you may be more attracted to meditation and that is a good time to start that.
There is nothing wrong with going straight into meditation if you have the calm disposition needed, and/or want to develop that straightaway. Paramahansa Yogananda (Diary of a Yogi) taught mostly meditation, and there are groups that focus heavily on meditation without any of the physical practice.

I couldn’t explain it better than @dabbler has above.

On a personal level, I practice both. After meditation, problems seem smaller and in perspective. I feel less overwhelmed by the big picture. I am less stressed, refreshed, I think much clearer, and the world seems to come at me at a speed in which I can handle. After meditating daily, this becomes the status quo and meditation is a way to maintain this feeling of well-being, of feeling at one with the whole, so to speak. Harmony in a inharmonious world.

Some days I won’t do the positions and just lay in the “death” position (my favorite) or sitting up with straight spine while I practice certain yoga breathing techniques (the pranayamas), but doing the positions you are most comfortable with is more effective. I also find certain pranayamas extremely effective for specific maladies when done properly. For instance, to combat insomnia, I will practice alternate nostril breathing and am asleep within minutes.

For times of extreme anxiety, especially due to sudden trauma, I find Ujjayi breathing extremely valuable and effective in reducing stress and excitement, to climb out of “Fight or Flight” mode, which we can find ourselves unnecessarily stuck in for extended periods long after the danger has passed.

A daily Ujjayi regime is now being recommended by therapists at some Veterans Administration hospitals to combat PTSD. Empirical evidence such as blood tests of patients using the technique have shown remarkable, positive physiological changes over a mater of days in PTSD patients stuck or easily triggered into Fight or Flight.

There are 3 interrelated parts to the yogic way of life. There is Ayurveda that is where you employ certain food, herbs and spices to properly nourish your body and bring it into balance so you are able to do the Asanas of yoga to your best ability. Your Yoga practice is what also physically balances your bodies muscles, organs and doshas/energy meridians to prepare your body and still your mind for Meditation. Of course you can do any of the 3 independently, but I always find my meditation to be much more effective after a yoga practice even if it is just a few asanas.

Meditation is mental hygiene.

It’s like brushing your teeth. Residues continually build up in the mind, like that scum that forms on your teeth through the day, only it’s a scum made of habitual thought patterns, opinions, prejudices, worries, etc. And, like dental plaque, if allowed to build up it becomes calcified and more difficult to remove, and will eventually cause real problems. Meditation, done regularly, helps dislodge this crap.

The “best” form of meditative practice is a very individual matter. At the core of most practices is a disciplined use of attention, bringing it to bear steadily on something other than the mental chatter running through your head. This can be done in a variety of ways though, and some people will have a greater affinity for one than another.

Choosing isn’t necessarily a matter of finding which practice you’re most comfortable with, or which one you like doing. The right practice for you will be one that challenges you. It will feel like work, not vacation. Sometimes it will engage you, spur your curiosity, intrigue you. But other times, it will feel flat, uninteresting and a chore. That’s all part and parcel of this kind of work. If you abandon a particular practice as soon as it starts to feel tough, then you’ll never benefit from it. It’s better to stick with any practice through thick and thin than to flit around, trying to find some hypothetical “perfect” fit for you.

I am not sure if you can do yoga without some amount of meditation.