According to the Oxford Dictionary of Buddhism:
"There is no word in English covering the same ground as duhkha in the sense it is used in Buddhism. The usual translation of 'suffering' is too strong, and gives the impression that life according to Buddhism is nothing but pain. As a consequence, some regard Buddhism as pessimistic.""(L)ike everything else," it is noted, "the individual ego is dependently originated and conditioned. Holding to the illusion of an independently originated self (atman), according to the Buddha, makes one crave for the satisfaction of this self. However, since everything is duhkha, and impermanent, there cannot be enduring satisfaction. Instead, craving (trsna) only leads to a vicious circle of unfulfilled, desires, and therefore more suffering (duhkha)."
"While duhkha certainly embraces the ordinary meaning of 'suffering,' it also includes deeper concepts such as impermanence (anitya) and unsatisfactoriness, and may be better left untranslated. The Buddha does not deny happiness in life, although this too is seen as part of duhkha because of its impermanence."
"The concept of duhkha is explained as having three aspects. Ordinary duhkha (duhkha-duhkha) refers to all kinds of suffering in life, such as illness, death, separation from loved ones, or not getting what one desires. The second aspect of duhkha, or duhkha produced by change (viparinama-duhkha) is the duhkha resulting from the impermanent nature of all things. The third aspect of duhkha, or duhkha as conditioned states (samskara-duhkha), is the most important philosophical aspect of the First Noble Truth. This teaches that what we call an 'individual' is, according to Buddhism, a combination of ever-changing physical and mental forces known as the 'five aggregates, (panca skandha). This is known as the doctrine of anatman, or no-self."
The second aspect of suffering - duhkha produced by change (viparinama-duhkha) - is somewhat more subtle, yet still very easy to grasp. Picture yourself on a paradaisical beach. Everything is beautiful and perfect. Then the thought arises that your vacation will end on Saturday and you will have to return to work and your 'normal' life. Suffering ensues. It ensues irrespective of whether we realize that we may not get something that we crave, or whether we realize that we may (or will) inevitably lose something that we cling to. Under these conditions, even that which is pleasurable causes the experience of suffering, albeit suffering produced by change - or viparinama-duhkha. This might be called "the suffering of impermanence."
The third aspect of suffering (samskara-duhkha) - suffering caused by the illusion that the ego-self is not conditioned or learned, but rather is actually 'who' and 'what' we are - is yet more subtle. Because of this mistaken illusion, we try to satisfy the ego's desires and allay its fears, but are ultimately unable to do so, as the ego itself is illusory. It is the ego-self that we mistake with our ultimate being - the Atman - a reality that is obscured by the conditioned states and thought patterns of the ego. This might be called "existential suffering."
To understand samskara-duhkha, it is perhaps helpful to examine what is meant by the 'samskaras' - a term that evolved, as did Buddhism, from the Vedic teachings of India.
Over time, our habitual thought patterns flow and eddy in particular forms, building up sand banks and pebble beds which both obscure the lake bottom and channel the water to run in certain directions. Prabhavananda identifies these obscurations as the samskaras. In our consciousness we identify with our samskaras (or thought-patterns) and lose all contact with our Ground of Being, the Atman. Thus, a person who is habitually involved with thoughts of those who have 'wronged' him, plotting revenge, becomes a resentful man. A person who habitually thinks anger thoughts becomes an angry man etc.
Even as we learn to still the thought waves in the mind through the practice of meditation and contemplation, the samskaras remain as obstacles to realizing 'who' and 'what' we are and achieving union with our Ground of Being. But, as time passes, and with disciplined practice, even the sandbanks and pebble beds of the samskaras will begin to dissipate.
No longer sustained and built up by our habitual, egoic thinking the samskaras fade in time, and once again we can see from our consciousness through the water-column of the mind to the Atman at the base. But, in the meantime, if we habitually identify with our samskaras as being 'who' and 'what' we are, we suffer. Like all other 'things,' our false ego-self is a product of dependent origination. If we can realize its impermanence and cease to identify with it we begin to overcome our samskara-duhkha.