This is explained by Piya Tan in his commentary on Dhatuvibhanga Sutta:
Maññassavāna-p,pavattanti, maññassave kho pana na-p,pavattamane. Here
maññassavā is resolved as mañña (“conceiving”) + assava (Skt āsrava),(a)
“purulent matter, discharge” (A 1:124); (b) tt for obstacle to
arhathood, “canker, influx, inflow, taint” (V 3:21 = 5:143 = A 5:70, V
5:225, D 3:216, M 1:55, S 5:410, Sn 535, Thī 76); also related to
āsava (spirituous liquor) because both are kept for a long time, MA
1:61 = AA 2:183 = ItA 1:114). The word assava is also related to
assavati,“it flows (on)”). In this context, pavattanti should be
rendered as “they flow” (S 2:31,J 2:104; PvA 143, 154, 198): M:ÑB
reading maññ‟ussavā (wr for maññ‟ussāvā): “the tides of
conceiving...sweep.”
Mental conceiving (mañña), closely related to “mental proliferation”
(papañca), here refers to thoughts and ideas arising from the three
roots of conceiving or mental proliferation: craving (taṇhā), view
(diṭṭhi) and conceit (māna) (Nm 280; Vbh 393; Nett 37 f). For an
interesting n on maññati, see M:ÑB 1162:n6. The “sage at peace” is the
arhat.
The term asava is usually translated as effluents or taints or defilements. You can read the question "What is effluent?"
When reading the Dhatuvibhanga Sutta (translated by Ven. Sujato), we find some details for this:
‘They have four foundations, standing on which the streams of
identification don’t flow. And when the streams of identification
don’t flow, they’re called a sage at peace.’ That’s what I said, but
why did I say it?
These are all forms of identifying: ‘I am’, ‘I am this’, ‘I will be’,
‘I will not be’, ‘I will have form’, ‘I will be formless’, ‘I will be
percipient’, ‘I will be non-percipient’, ‘I will be neither percipient
nor non-percipient.’ Identification is a disease, a boil, a dart.
Having gone beyond all identification, one is called a sage at peace.
The sage at peace is not reborn, does not grow old, and does not die.
They are not shaken, and do not yearn. For they have nothing which
would cause them to be reborn. Not being reborn, how could they grow
old? Not growing old, how could they die? Not dying, how could they be
shaken? Not shaking, for what could they yearn?
It sounds to me like maññassava is more or less the same as bhavāsava, the effluent or taint or defilement of becoming or being.
This can be found in MN 9 (translated by Ven. Bodhi):
“And what are the taints, what is the origin of the taints, what is
the cessation of the taints, what is the way leading to the cessation
of the taints? There are these three taints: the taint of sensual
desire, the taint of being, and the taint of ignorance. With the
arising of ignorance there is the arising of the taints. With the
cessation of ignorance there is the cessation of the taints. The way
leading to the cessation of the taints is just this Noble Eightfold
Path; that is, right view, right intention, right speech, right
action, right livelihood, right effort, right mindfulness, and right
concentration.
And also AN 6.63 (translated by Ven. Thanissaro):
“There are these three kinds of defilements: the defilement of
sensuality, the defilement of becoming, the defilement of ignorance.
“And what is the cause of defilements? Ignorance is the cause of
defilements.
“And what is the diversity in defilements? There are defilements that
lead to hell, those that lead to the animal womb, those that lead to
the realm of the hungry shades, those that lead to the human world,
those that lead to the world of the devas. This is called the
diversity in defilements.
“And what is the result of defilements? One who is immersed in
ignorance produces a corresponding state of existence, on the side of
merit or demerit. This is called the result of defilements.
“And what is the cessation of defilements? From the cessation of
ignorance is the cessation of defilements; and just this noble
eightfold path—right view, right resolve, right speech, right action,
right livelihood, right effort, right mindfulness, right samādhi—is
the way leading to the cessation of defilements.
