I'm not sure who wrote the short introduction at the top of the Dukkha page of AccessToInsight.org but it is a very appropriate comment to your question:
No single English word adequately captures the full depth, range, and
subtlety of the crucial Pali term dukkha. Over the years, many
translations of the word have been used ("stress,"
"unsatisfactoriness," "suffering," etc.). Each has its own merits in a
given context. There is value in not letting oneself get too
comfortable with any one particular translation of the word, since the
entire thrust of Buddhist practice is the broadening and deepening of
one's understanding of dukkha until its roots are finally exposed
and eradicated once and for all. One helpful rule of thumb: as soon as
you think you've found the single best translation for the word, think
again: for no matter how you describe dukkha, it's always deeper,
subtler, and more unsatisfactory than that.
You must remember that this is a technical term that goes beyond the ordinary meaning of the word in Pali.
The canonical definition is:
"Birth is dukkha, aging is dukkha, death is dukkha; sorrow,
lamentation, pain, grief, & despair are dukkha; association with the
unbeloved is dukkha; separation from the loved is dukkha;
not getting what is wanted is dukkha. In short,
the five clinging-aggregates are dukkha."
— SN 56.11
That's quite self-explanatory. But if you want a further explanation, just look at the Dukkha page for Ven. Sariputta's elaboration.
Ven. Bodhi's comments from the forum on Understanding Dukkha:
In the Pali suttas, the discourses of the Buddha, the word dukkha is
used in at least three senses. One, which is probably the original
sense of the word dukkha and was used in conventional discourse
during the Buddha’s time, is pain, particularly painful bodily
feelings. The Buddha also uses the word dukkha for the emotional
aspect of human existence. There are a number of synonyms that
comprise this aspect of
dukkha: soka, which means sorrow; aryadeva, which is lamentation;
dolmenasa, which is sadness, grief, or displeasure; and upayasa,
which is misery, even despair. The deepest, most comprehensive aspect
dukkha is signified by the term samkara-dukkha, which means the dukkha that is inherent in all conditioned phenomena simply by virtue of the fact that they are conditioned.
This means that the technical term dukkha has a superficial meaning which is pain, suffering, stress, lamentation, sorrow, grief, despair, anguish, dissatisfaction, encountering that which is disliked, being separated from that which is liked, and not getting something you want.
However, the technical term dukkha also has a deeper meaning in sankhara-dukkha - which is that all conditioned phenomena are impermanent, and therefore is a cause of suffering, because "they cannot provide stable happiness and security" (see below). It is for this reason that some people say "unsatisfactoriness" is a better term to use than "suffering" to explain the deeper meaning.
The superficial meaning covers only the negative experiences, while the deeper meaning covers the fact that positive and neutral experiences cannot be sustained forever, and negative experiences cannot be avoided forever.
In "Anicca Vata Sankhara", Ven. Bodhi comments:
The most important fact to understand about sankharas, as
conditioned formations, is that they are all impermanent:
"Impermanent, alas, are formations." They are impermanent not only in
the sense that in their gross manifestations they will eventually come
to an end, but even more pointedly because at the subtle, subliminal
level they are constantly undergoing rise and fall, forever coming
into being and then, in a split second, breaking up and perishing:
"Their very nature is to arise and vanish." For this reason the Buddha
declares that all sankharas are suffering (sabbe sankhara dukkha)
— suffering, however, not because they are all actually painful and
stressful, but because they are stamped with the mark of transience.
"Having arisen they then cease," and because they all cease they
cannot provide stable happiness and security.
To win complete release from suffering — not only from experiencing
suffering, but from the unsatisfactoriness intrinsic to all
conditioned existence — we must gain release from sankharas. And
what lies beyond the sankharas is that which is not constructed, not
put together, not compounded. This is Nibbana, accordingly called the
Unconditioned — asankhata — the opposite of what is sankhata, a
word which is the passive participle corresponding to sankhara.
Nibbana is called the Unconditioned precisely because it's a state that is neither itself a sankhara nor constructed by sankharas; a
state described as visankhara, "devoid of formations," and as
sabbasankhara-samatha, "the stilling of all formations."