The mental act of noting is important to know the object clearly. Each object, whether that is pain, hearing, or thinking, etc., should be known as it occurs in the present moment.
When we are day-dreaming, there is very little awareness — we are lost in thoughts and fantasies. When we are remembering some sensual pleasures enjoyed earlier, we are not being mindful of the present moment. When we are planning some activity in the future, the mind is imagining.
The mental noting or labelling, brings the mind to the present, to become aware of what is going on in our mind — the awareness knows it as a mental process, and the mind is no longer lost in concepts, but knows realities in the present.
In terms of the five factors of concentration (jhāna),
the mental noting is called initial application (vitakka).
If the awareness is fixed firmly on each new mental object without wandering here and there, then that is the factor of sustained application (vicāra).
The beginner in meditation experiences plenty of pain, wandering thoughts, restlessness, drowsiness, and doubt (indecision). As his/her concentration develops, the wandering thoughts diminish, and awareness is established. That's what “satipatthāna”
means — to establish awareness or mindfulness in the present moment.
Gradually, the hindrances to concentration are overcome, and the mind settles in the present moment. It doesn't mean that the meditator is only aware of the rising and falling movements of the abdomen. The mind may stay for a few breaths only, before some other object occurs such as pain, hearing, or thinking. However, the mature meditator does not become distracted by these secondary meditation objects, but quickly notes them as each occurs. Automatically, when the secondary objects have ceased or faded into the background, the awareness returns to focus on the abdominal movements.
Later, the meditator experiences joy (pīt),
and one-pointedness (ekaggatā),
which are the other three factors of concentration, but to get to that stage we have to work patiently to overcome the five hindrances — sensual desire, ill-will, sloth, restlessness, and doubt. Each time these arise, they too must be noted with bare awareness.
You can find many books by the late Venerable Mahāsī Sayādaw
on my web site. Read a little, but practise a lot. Too much reading can just add to the mental distraction. A little regular reading helps to clarify and focus the attention on what is important.