As you progress in your meditation practice, the use of mantra(s) is a powerful way to stay focused all day.
I recall reading that Ram Dass said that even when he is speaking or listening to others, that in the background his mantra is always running in his head: “Ram ... Ram ... Ram.”
In the excellent book, Practicing the Jhanas, I throughout your day that you constantly remember to bring your attention back to the Anapana spot, a spot just under your nose.
When I visited the Providence Zen Center, I was instructed to constantly question, “What am I?” If I was walking I would constantly ask myself that question, and if I was driving I would ask, “Who is driving,” and if I was doing the dishes I would ask, “Who is washing,” etc.
The thing I find about any of these mantras or mindfulness approaches is that they help to keep the mind focused more throughout the day. The benefit of this is that the more you stay focused during the day, the quicker you’ll be able to get into deep meditation states when you start meditating.
Think of it this way: If 100 is a perfect score in meditation — the deepest you can get — if you don’t use mantras during the day, when you sit down to meditate, you’re starting at Level 0, so you have a long way to get to Level 100. But if you use mantras during the day you can keep yourself at some other level. It may be 10, 20, or 80, but either way, when you sit down to start meditating, you’re already down the road, much closer to 100 than you would be otherwise.
So, in summary, constant use of mantras during the day help to keep your mind focused, so when you sit down to meditate, you’ll find that you’ve already been meditating throughout the day, and you will more easily and quickly move into deeper meditation states.
(Another benefit is that you will eventually be more ready to experience what Katsuki Sekida calls positive samadhi. He refers to absolute samadhi as being a deep state of meditation while in seated meditation, and positive samadhi is a similar state as you go about your daily life. See the book Zen Training for more details.)