There are at least two ways to practice Anapanasati, - with a focus on samatha (jhana, samadhi) and with a focus on vipassana.
The difference between samatha and vipassana practices of Anapanasati is explained on the page 23 of the book "In This Life Itself" by Ven. Dhammajiva:http://www.vipassana.com/meditation/dha ... /index.php
Samadhi is when the totality (kasina) of perception is coloured by the basis (arammana) of concentration, as described in Kosala sutta:
"There are these ten totality-dimensions. Which ten? One perceives the earth-totality above, below, all-around: non-dual, unlimited. One perceives the water-totality... the fire-totality... the wind-totality... the blue-totality... the yellow-totality... the red-totality... the white-totality... the space-totality... the consciousness-totality above, below, all-around: non-dual, unlimited. These are the ten totalities."http://www.accesstoinsight.org/tipitaka ... .than.html
The reason of establishing remembrance (sati) in the area between the mouth and the nostrils ('parimuhkhaṃ
', as described in Anapanasati sutta) is to acquire the nimitta (perceptual image) of air, since the Anapanasati jhana is based on the element of air:
Pakatiassāsapakatipassāse nissāya uppannanimittampi assāsapassāsāti nāmaṃ labhati. Upaṭṭhānaṃ satīti taṃ ārammaṇaṃ upecca tiṭṭhatīti sati upaṭṭhānaṃ nāma.
"Sati upatthana" means that 'sati', having approached, is established on that basis (arammana), - nimitta (perceptual image), that arises due to natural inbreath and outbreath.
Kiṃ pana pathavīkasiṇaṃ ādiṃ katvā aṭṭhikasaññāpariyosānāvesā rūpāvacarappanā, udāhu aññāpi atthīti? Atthi; ānāpānajjhānañhi kāyagatāsatibhāvanā ca idha na kathitā. Kiñcāpi na kathitā vāyokasiṇe pana gahite ānāpānajjhānaṃ gahitameva; vaṇṇakasiṇesu ca gahitesu kesādīsu catukkapañcakajjhānavasena uppannā kāyagatāsati, dasasu asubhesu gahitesu dvattiṃsākāre paṭikūlamanasikārajjhānavasena ceva navasivathikāvaṇṇajjhānavasena ca pavattā kāyagatāsati gahitāvāti. Sabbāpi rūpāvacarappanā idha kathitāva hotīti.
"But is this all the absorption belonging to the consciousness of the sphere of refined form, beginning with the earth kasiṇa and ending in the perception of the skeleton? Or is there anything else?"
"Yes, there is. There is ānāpāna jhāna and the development of kāyagatāsati, which have not been spoken of here."
"Because ānāpāna jhāna is included in the air kasiṇa; the development of kāyagatāsati arisen by virtue of the fourfold and fivefold jhānas with reference to the hair etc., is included in the colour kasiṇas; the kāyagatāsati produced by virtue of the jhānas attending to the unattractiveness in the thirty-two parts of the body, and that of the jhāna attending to the colours of the nine kinds of corpses in the charnel grounds is included in the ten repulsive things. Thus all the absorptions of consciousness connected with the sphere of refined form have been included here."
For practical descriptions of how this can be done, in the case of air, see:
De-perception by Thanissaro Bhikkhuhttp://www.accesstoinsight.org/lib/auth ... ption.html
Anapanasati chapter of Vimuttimaggahttp://www.archive.org/details/ArahantU ... reedom.pdf
One has to tune in the "airiness" of the air, and gradually spread it all over the body, as Ajahn Lee Dhammadharo describes:
"When you see that a nimitta has appeared, mindfully focus your awareness on it — but be sure to focus on only one at a time, choosing whichever one is most comfortable. Once you've got hold of it, expand it so that it's as large as your head. The bright white nimitta is useful to the body and mind: It's a pure breath that can cleanse the blood in the body, reducing or eliminating feelings of physical pain."http://www.accesstoinsight.org/lib/thai/lee/inmind.html
The initial perceptual image of the air, thanks to which such 'colouring' of the perception can be done, is called 'nimitta'. This term is mentioned in the suttas in the context of jhana, as for example in the Gavi sutta:http://www.accesstoinsight.org/tipitaka ... .than.html
and elsewhere - see the thread:viewtopic.php?f=23&t=2770
Unfortunately, later the sense of the term 'nimitta' was pretty much lost. But it has been regained, for example, in the Pa Auk Sayadaw lineage.