The terms "conditioned" and "compounded" are often used to explain the term "sankhara".
Conditioned means phenomena which are affected or caused by each other. For e.g. a tree is not just a standalone object. It is dependent on sunlight, water, air etc. Space and time too are conditioned as we can see in Einstein's Theory of General Relativity.
The following writing entitled "The Fullness of Emptiness" by Thich Nhat Hanh explains this nicely:
If you are a poet, you will see clearly that there is a cloud floating
in this sheet of paper. Without a cloud, there will be no rain;
without rain, the trees cannot grow; and without trees, we cannot make
paper. The cloud is essential for the paper to exist. If the cloud is
not here, the sheet of paper cannot be here either. ....
If we look into this sheet of paper even more deeply, we can see the
sunshine in it. If the sunshine is not there, the forest cannot grow.
In fact, nothing can grow. Even we cannot grow without sunshine. So we
know that the sunshine is also in this sheet of paper. ....
And if we continue to look, we can see the
logger who cut the tree and brought it to the mill to be transformed
into paper. And we see the wheat. We know that the logger cannot exist
without his daily bread, and therefore the wheat that became his bread
is also in this sheet of paper. And the logger’s father and mother are
in it too. When we look in this way, we see that without all of these
things, this sheet of paper cannot exist.
The Fullness of Emptiness
The term compounded explains how phenomena is composed of other phenomena and are not standalone. For e.g. a tree has water and gases in it. Molecules can be broken down into atoms and atoms can be broken down into subatomic particles. And all of these are also conditioned.
The sutta below provides an explanation of what is meant by compounded but also explains what is convention.
A chariot is never standalone. It is an assemblage or composition of different parts, like wheels, axle etc. The term "chariot" is therefore a convention that we use to describe this composition. If one wheel is missing, or replaced, it is still called a "chariot". But if all parts are disassembled, then we don't call it a "chariot" anymore.
So, the term "chariot" is a convention used to describe an object that is compounded by many parts.
Similarly, a "being" (satta) is the convention used when the five aggregates of form, feeling, perception, consciousness and mental formations are present together and functioning. A "being" is therefore compounded.
Then the bhikkhuni Vajira, having understood, "This is Mara the
Evil One," replied to him in verses:
Why now do you assume 'a being'?
Mara, have you grasped a view?
This is a heap of sheer constructions:
Here no being is found.
Just as, with an assemblage of parts,
The word 'chariot' is used,
So, when the aggregates are present,
There's the convention 'a being.'
It's only suffering that comes to be,
Suffering that stands and falls away.
Nothing but suffering comes to be,
Nothing but suffering ceases.
Then Mara the Evil One, realizing, "The bhikkhuni Vajira knows me,"
sad and disappointed, disappeared right there.
The sutta below gives the analogy of a stringed musical instrument, called the lute (vina). It can produce music. But if you break down the lute into its constituent parts and air, you cannot find music anywhere. Music is both conditioned and compounded by the different parts of the lute, and even the actions of the lute player. Music is made up of rythmic sound composed of movement of air. And this movement is dependent on the movement and vibration of parts of the lute.
Similarly, the mental idea of the self is conditioned and compounded by the five aggregates of form, feeling, perception, consciousness and mental formations. Dependent origination (paticcasamuppada) is the Buddha's explanation of how the birth of the mental idea of the self is conditioned by the five aggregates. But it's also compounded, because the mental idea of the self is also a type of thought, a mental formation.
"Suppose there were a king or king's minister who had never heard the
sound of a lute before. He might hear the sound of a lute and say,
'What, my good men, is that sound — so delightful, so tantalizing, so
intoxicating, so ravishing, so enthralling?' They would say, 'That,
sire, is called a lute, whose sound is so delightful, so tantalizing,
so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go
& fetch me that lute.' They would fetch the lute and say, 'Here, sire,
is the lute whose sound is so delightful, so tantalizing, so
intoxicating, so ravishing, so enthralling.' He would say, 'Enough of
your lute. Fetch me just the sound.' Then they would say, 'This lute,
sire, is made of numerous components, a great many components. It's
through the activity of numerous components that it sounds: that is,
in dependence on the body, the skin, the neck, the frame, the strings,
the bridge, and the appropriate human effort. Thus it is that this
lute — made of numerous components, a great many components — sounds
through the activity of numerous components.'
"Then the king would split the lute into ten pieces, a hundred pieces.
Having split the lute into ten pieces, a hundred pieces, he would
shave it to splinters. Having shaved it to splinters, he would burn it
in a fire. Having burned it in a fire, he would reduce it to ashes.
Having reduced it to ashes, he would winnow it before a high wind or
let it be washed away by a swift-flowing stream. He would then say, 'A
sorry thing, this lute — whatever a lute may be — by which people have
been so thoroughly tricked & deceived.'
"In the same way, a monk investigates form, however far form may go.
He investigates feeling... perception... fabrications...
consciousness, however far consciousness may go. As he is
investigating form... feeling... perception... fabrications...
consciousness, however far consciousness may go, any thoughts of 'me'
or 'mine' or 'I am' do not occur to him."
Nibbana is the only phenomena which is not conditioned. It is also not compounded. This can also be inferred from the three marks of existence, as found in this answer.
“There is, mendicants, an unborn, unproduced, unmade, and
unconditioned (asaṅkhataṁ). If there were no unborn, unproduced,
unmade, and unconditioned, then you would find no escape here from the
born, produced, made, and conditioned. But since there is an unborn,
unproduced, unmade, and unconditioned, an escape is found from the
born, produced, made, and conditioned.”
The term asaṅkhata seems to mean unconditioned and also uncompounded, according to the PTS Pali-English dictionary:
Sankhata Sankhata [pp. of sankharoti; Sk. saŋskṛta] 1. put together,
compound; conditioned, produced by a combination of causes, "created,"
brought about as effect of actions in former births S ii.26; iii.56;
Vin ii.284; It 37, 88; J ii.38; Nett 14; Dhs 1085; DhsA 47. As nt.
that which is produced from a cause, i. e. the sankhāras S i.112; A
i.83, 152; Nett 22. asankhata not put together, not proceeding from a
cause Dhs 983 (so read for sankhata), 1086; Ep. of nibbāna "the
Unconditioned" (& therefore unproductive of further life) A i.152; S
iv.359 sq.; Kvu 317 sq.; Pv iii.710 (=laddhanāma amataŋ PvA 207); Miln
270; Dhs 583 (see trsln ibid.),