Insight into the dissatisfaction that is unavoidable when we desire and cling to conditioned phenomena is a direct result of clearly seeing impermanence. The Pali term dukkha can be translated in various ways according to the context, but the most basic meaning of dukkha is 'pain.' Pain can be either physical pain or mental pain.
Now the very fact that the body is a conditioned fabrication means that it will experience pain. This can be intense pain as in the case of serious accident or sickness, but dukkha in this context also refers to the many more or less minor aches and pains that are more like irritations really. And the mind, not wanting to experience the unpleasant feeling (vedana) that such physical irritation gives rise to, is constantly trying to avoid all such irritation. When we've been in one position too long, we change position, often without even realizing that we're doing so. When we feel the first sensations of hunger or thirst, we get something to eat or drink etc., etc.. And on and on goes the continual search for physical comfort and security.
Mental pain can also be very intense, as a result of a sudden loss such as the death of a loved one, or the loss of a job or financial difficulties, or even the notion that we've suffered some loss in social stature or reputation. Anger, jealousy, and fear are all intense fabricated phenomena experienced as mental pain. If we've ever taken the time to consciously experience such conflicting emotions (kilesa) as they're happening we can see this suffering clearly. Also, over and above these common disturbances, mental illness can cause unspeakable pain and suffering. But here again, more often than not, mental pain manifests as the many more or less minor frustrations, stresses, and irritations that assault the untrained mind.
But the Buddha's insight into suffering as the first noble truth goes deeper than this, and involves the understanding that identifying with even pleasurable conditioned states will lead to eventual frustration and disappointment because these too are conditioned phenomena which are inconstant and therefore don't last. There's nothing wrong with happiness as such. Actually, discovering which volitional thoughts, spoken words, and actions lead to more stable experiences of happiness is a large part of the noble path. But the important thing to keep in mind is that one shouldn't identify with even these productive and skillful activities, such as refined meditative states, and grasp them as some sort of cocoon to somehow escape the conditioned world. All such egoistic motivations of grasping and seeking only promotes further frustration and dissatisfaction, because even these existential states are conditioned and therefore impermanent. All such seeking is what keeps the samsaric system operating through continued craving, grasping, and becoming. And it's the ending of clinging to any and all conditioned phenomena that the Buddha calls the deathless (amata) liberation of mind (cittassa vimokkha).
So we can see that egoistic seeking and identification with conditioned phenomena of body and mind always results in disappointment and dissatisfaction, because phenomena are inconstant and forever changing. And for this reason they are unsatisfactory, which seems to be a pretty good general purpose translation of dukkha. But along with this connotation of general unsatisfactoriness, we can also keep in mind the above mentioned statement from the Silavant Sutta, where the Buddha describes conditioned phenomena in no uncertain terms as:
[S]tressful, a disease, a cancer, an arrow, painful, an affliction....
Therefore, the truth of suffering (dukkha sacca) involves clearly seeing and thereby discerning that because all conditioned phenomena are impermanent, they are unsatisfactory.