The neither-pleasant-nor-painful feelings also known as neutral feelings is one of three types of feeling including pleasant and painful. Feelings here means sensations experienced by the six senses (including the mind).
The definition of neutral feeling comes in MN 44 and also states its relationship to ignorance:
Neutral feeling is pleasant when there is knowledge, and painful when
there is ignorance.”
“The underlying tendency for greed underlies pleasant feeling. The
underlying tendency for repulsion underlies painful feeling. The
underlying tendency for ignorance underlies neutral feeling.”
In Contemplation of Feeling, Nyanaponika Thera explained this:
Pleasant feeling is habitually linked with enjoyment and desire;
unpleasant feeling with aversion; neutral feeling with boredom and
confusion, but also serving as background for wrong views.
Also in SN 36.5:
“Mendicants, there are these three feelings. What three? Pleasant,
painful, and neutral feeling. Pleasant feeling should be seen as
suffering. Painful feeling should be seen as a dart. Neutral feeling
should be seen as impermanent. When a mendicant has seen these three
feelings in this way, they’re called a mendicant who has cut off
craving, untied the fetters, and by rightly comprehending conceit has
made an end of suffering.
The neither-pleasant-nor-painful feelings also known as neutral feelings, normally make us bored or dissatisfied. Cravings would lead one to seek pleasures (kama tanha) or to become something or achieve something (bhava tanha) rather than sit around all day experiencing neutral feelings that don't bring satisfaction.
No feelings at all, would also be a cause for boredom and dissatisfaction. From the same article by Nyanaponika Thera, we read the commentary of the suttas and his comment:
Comy.: "From the fourth Jhana onwards, it is the
neither-painful-nor-pleasant feeling (that is present in these
meditative states). But this neutral feeling, too, is called
'pleasure' (sukha), on account of its being peaceful and sublime. What
arises by way of the five cords of sensual desire and by way of the
eight meditative attainments is called 'pleasure as being felt'
(vedayita-sukha). The state of Cessation of Perception and Feeling is
a 'pleasure, not being felt' (avedayita-sukha). Hence, whether it be
pleasure felt or not felt, both are assuredly 'pleasure,' in the sense
of their being painfree states (niddukkhabhava-sankhatena sukhena)."
In AN 9.34, the venerable Sariputta exclaims: "Nibbana is happiness,
friend; Nibbana is happiness, indeed!" The monk Udayi then asked: "How
can there be happiness when there is no feeling?" The venerable
Sariputta replied: "Just this is happiness, friend, that therein there
is no feeling."
To the arahant, neutral feelings, no feelings and Nibbana are all pleasant.