One of the most striking benefits of meditation is the increased inner peace and inner poise that result from meditation. This benefit is not instantaneous but gradually increases with our meditation practice. The peace that we gain from meditation then stays with us. We can then deal with other circumstance with greater detachment and poise. This is one of the real practical benefits of meditation. This is an extract from Sri Chinmoy Library in which Sri Chinmoytalks about this particular benefit of meditation
Interviewer: One can obtain peace for a moment but then when he goes out from here, he will go back to the same hustle of human life.
Sri Chinmoy: This happens to ordinary people. You have to know that there is a big difference between a really spiritual person and one who only goes to church to pray for half an hour, obtains a little peace and then goes to the coffee shop and gives his peace to the coffee shop. But if he meditates for long hours and establishes this practice firmly, then he will get durable results. If you start to run, you will not do it very well for the first few days. The same thing with dancing or any other activity. Only continuous practice will give you satisfactory results. The same thing happens in the spiritual life. When you are advanced you can retain the benefits for a long period of time, but not at the beginning. What you say is absolutely right, you obtain peace for a moment and when you go again to the world, restlessness comes back to you. But if you can enter into the deepest world and stay there for some time during your meditation, a day will come when, in the midst of the outside world, in front of people, speaking with people, mixing with people, you will possess your own deepest Peace. This Peace remains imperturbable, unmoveable.
Excerpt from Earth’s Cry Meets Heaven’s Smile, Part 3 by Sri Chinmoy.
As well as inner peace, meditation can also give us many other benefits such as relief of stress, better health and also the joy that comes from experiencing contact with our inner self our soul.
another article on benefit of meditation