Calm-abiding meditation is the practice of bringing stillness and clarity to the mind by gentle and continuous focus on a single object. The most common object of concentration is the breath.
I am not a Buddhist teacher and I may be mistaken about these things. I am simply reporting what I have learned through direct experience during almost two years of daily meditation practice. Point (4) contains normative statements about which I am not absolutely confident.
(1) The mind is susceptible to capture by discursive thought, even when there is a determined effort to concentrate. This slipping into thought leaves no trace and makes no signal; the moment of its beginning cannot be found on reflection and it has no discernible cause. Becoming lost in thought is like falling asleep: the silent transition into unawareness passes undetected by the mind. Coming back to focus has the feeling of waking from a dream.
(2) Thought is seductive. There is the feeling of wanting to hold onto it, as if it were precious and important. Turning the mind once more to focus on the breath takes effort. Putting down should be easy, and picking up hard. With thought, however, it is the opposite.
(3) There is a period when the mind begins to stabilize on the breath and to quieten that it is particularly susceptible to capture by thinking, i.e., before the mind "locks on" properly. It seems that when the mind has just become quiet, it is vulnerable even to "little" thoughts that normally would have been tiny bubbles below the surface of consciousness. In the quiet moment just before concentration is fully established, these rise up and draw attention very easily. This causes the sensation of whimsical day-dreaming that feels, on reflection, very much like the period between waking and sleeping.
(4) Focus is not a goal in and of itself. It is a means, a gateway, into discovering the nature of mind. That being said, even brief periods of focus can give rise to ecstatic states and phsical sensations, like warmth throughout the body, tingling and crawling of the skin, and flashes of light behind closed eyelids. A gentle, but insistent, returning to the breath is almost guaranteed to produce these sensations eventually. As pleasurable as these feelings may be, they are incidental and should not be sought after for their own sake.
(5) There is a sense of directed attention at the breath, which produces a narrow, closed-in focus, but this can be opend up into a wide, transparent focus by settling back and allowing the sensation of the breath to "fall into" awareness. This opening up may be accompanied by the euphoric sensations described above.