In summary it seems to mean approximately the same thing as a "fetter".
There's a definition of āsava in the Manual of Buddhist Terms and Doctrines by Maha Thera Nyanatiloka, which is copied into the Dhamma Wiki.
The definition in the Dhamma Wiki is almost the same as in the manual, except that in the Wiki there is added an example of each of the four types. I think an example helps make it easier to understand:
- The mental fermentation of sense-desire kāmāsava, Ex: 'All is pleasant'
- The mental fermentation of desiring existence bhavāsava, Ex: 'Being is good'
- The mental fermentation of wrong views ditthāsava, Ex: 'My opinion is best'
- The mental fermentation of ignorance avijjāsava. Ex: 'Suffering exists not'
The term "āsava" is also introduced in the dharmafarer translation of the Jhāna Sutta (AN 9.36), including,
As “mental influxes,” the oldest list is probably the set of 3 influxes—of sense-desire
(kām’āsava), of existence (bhav’āsava), and of ignorance (avijjâsava)
-- which are essentially the same
as the 3 graspings (ti,gaha) of craving (tanhā), conceit (mana) and views (ditthi), on account of which
arise, resp, the notions “this is mine,” “this I am,” and “this is my self”), such as in the Vatthûpama
Sutta (M 7).
The second half of the Dhamma Wiki definition says that these are destroyed at various stages of enlightenment, e.g. Stream Entry:
Through the path of Stream-Entry, the fermentation of views is destroyed; Through the path of Non-Returning, the fermentation of sense-desire; Through the path of Arahatship, the fermentations of existence and ignorance. M. 2 shows how to overcome the fermentations, namely, through insight, sense-control, avoidance, wise use of the necessities of life.
I think this implies that these four asavas correspond to, are not different than, four of the ten fetters.
The Sabbasava Sutta (MN 2) implies that beyond these four there are other asavas, for example ill-will (which too corresponds to another of the ten fetters)
Reflecting appropriately, he does not tolerate an arisen thought of ill will...
The introduction to the dharmafarer translation of the Sabbāsava Sutta (MN 2) describes asavas in even more detail, including,
Apparently, the three influxes were in due course expanded into the ten fetters.
This Manual of Abhidhamma (on page 365) contains another definition of asava:
âsavà— is derived from à +√ su, to flow. They
are so called either because they flow up to the topmost plane
of existence or because they persist as far as the Gotrabhå
consciousness (i.e., the thought-moment that immediately
precedes the Path-consciousõess of the ‘Stream-Winner’—
Sotàpatti). These âsavas are latent in all worldlings and may
rise to the surface in any plane of existence. They lie dormant
in all from an indefinite period and are treated as strong
intoxicants or drugs that infatuate beings. Defilements,
Corruptions, Depravities, Taints, Intoxicants, Stains are suggested
as the closest equivalents for this ‘infamously famous’
Pàli term. See Compendium, p. 170, n. 1, p. 227.
Of the four âsavas kàmàsava means attachment to
sensual pleasures, bhavàsava is attachment to Råpa and
Aråpa planes of existence, diññhàsava are the sixty-two kinds
of erroneous views (see Brahmajàla Sutta, DN1), and avijjàsava is ignorance with
regard to the four Noble Truths, past life, future life, both
past and future lives, and the Law of Dependent Arising.
The "Compendium" which is referenced above is the PTS Compendium of Philosophy, which says it's difficult to translate:
We agreed to let this term, infamously famous, remain
untranslated. Nothing to fit has yet been discovered.
Warren's 'depravities' and Neumann's 'Wähnen' make
no pretence to be literal. 'Floods' and 'Taints' (Rhys
Davids) convey the idea of spreading movement, of
disaster, of defilement, my 'Intoxicants' and 'Drugs'
that of poison. The former idea seems alone active in the
minds of the Commentators; and yet,
if A. i., 124, § 7, be compared with Jataka IV., 222 (3):
There is in the world an Asava1 called strong drink,
1 Jataka Commentary: i.e. 'a poison' (visaij), from flower-asava and the like.
the latter idea may claim some canonical support (cf. Dialogues of the Buddha, i. 92 ; ii. 28). To the general
Buddhist, Asava probably conveyed no more 'visualizable' meaning than sin does to the Christian, although,
in either case, the moral vibration in consciousness is heavy
enough.
Different suttas describe how to end the asavas; for example:
The Sabbasava Sutta (MN 2), which starts with:
The Blessed One said, "Monks, the ending of the fermentations is for one who knows & sees, I tell you, not for one who does not know & does not see. For one who knows what & sees what? Appropriate attention & inappropriate attention. When a monk attends inappropriately, unarisen fermentations arise, and arisen fermentations increase. When a monk attends appropriately, unarisen fermentations do not arise, and arisen fermentations are abandoned. There are fermentations to be abandoned by seeing, those to be abandoned by restraining, those to be abandoned by using, those to be abandoned by tolerating, those to be abandoned by avoiding, those to be abandoned by dispelling, and those to be abandoned by developing.
The rest of the sutta gives example of inappropriate and appropriate attention.
The dharmafarer introduction to this sutta has 15 pages, and among other things it tries to show that these methods correspond to the various factors of the noble eightfold path.
Incidentally the example in the sutta of "attending appropriately" is,
He attends appropriately, This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress. As he attends appropriately in this way, three fetters are abandoned in him: identity-view, doubt, and grasping at precepts & practices. These are called the fermentations to be abandoned by seeing.
The Jhana Sutta (AN 9.36), which starts with:
"I tell you, the ending of the mental fermentations depends on the first jhana... the second jhana... the third... the fourth... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness. I tell you, the ending of the mental fermentations depends on the dimension of neither perception nor non-perception.
The dharmafarer introduction to this sutta says,
The (Āsava-k,khaya) Jhāna Sutta (A 9.36) describes
the attainment of arhathood or non-return through meditation that applies calm (samatha) as a
basis for insight (vipassanā). This is one of the four approaches or strategies to meditation as laid out by
Ānanda in the (Yuganaddha) Paṭipadā Sutta (A 4.170), makes a very clear reference to the various
vehicles for mental cultivation for the attaining of arhathood, as follows:
- Insight preceded by calm.
When the path arises in him, he pursues it, so that the mental
fetters are abandoned and the latent tendencies are destroyed.
- Calm preceded by insight.
When the path arises in him, he pursues it, so that the mental
fetters are abandoned and the latent tendencies are destroyed.
- Calm and insight coupled together.
When the path arises in him, he pursues it, so that the
mental fetters are abandoned and the latent tendencies are destroyed.
- A monk’s mind is seized by agitation caused by higher states of mind;
but there comes a
time when his mind becomes internally steadied, composed, unified and concentrated. Then the
path arises in him, and while he does so, the fetters are abandoned and the latent tendencies are
destroyed.