What is the meaning of the word suffering or (pali) dukkha when it is referred to in topics around Dhamma and Vinaya or Buddhism?
Dukkha is the characteristic of all human experiences (or what is felt) either pleasant, painful or neutral. Pain is Dukkha in it's own right. Parting with pleasantness is Dukkha. Also any conditioned existance is Dukkha even in the neutral experiences as becoming is present which has inherent suffering like birth, aging, painful life experiences and death .
According to the Suttas, there are three categories of Dukkha:
"There are these three forms of [Dukkha], my friend: the [Dukkha] of pain, the [Dukkha] of fabrication, the [Dukkha] of change. These are the three forms of [Dukkha]." http://www.accesstoinsight.org/tipitaka/sn/sn38/sn38.014.than.html
(I've put in the original Pali for the sake of clarity)
Dukkha of pain refers to when something is literally painful either physically or emotionally. When I stub my toe or feel sad or upset, that is the Dukkha of pain.
The Dukkha of fabrication is a deep existential thing. It means that all fabricated things (i.e. everything that comes about through causes and conditions) cannot give us the happiness we want from it. That doesn't mean that everything is painful, but rather that everything is imperfect.
The Dukkha of change refers to the fact that pleasant things change. I like ice cream, but eventually I will eat the whole thing. This fact is called the Dukkha of change.
It is very important to understand that when Buddhist texts say that all formations are Dukkha, they always mean it in the sense of the Dukkha of formations or the Dukkha of change, not the Dukkha of pain, because obviously there are things in the world that are pleasurable.
Definition of dukkha
This article, Dukkha, is a page of references to three or four suttas which define dukkha.
The first definition on that page is the description of the First Noble Truth, in the Dhammacakkappavattana Sutta:
Now this, monks, is the noble truth of stress: Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with the unbeloved is stressful, separation from the loved is stressful, not getting what is wanted is stressful. In short, the five clinging-aggregates are stressful.
Sariputta's elaboration describes all these various terms in more detail.
I'm used to thinking of dukkha as, "the First Noble Truth", but perhaps I should note that it's not the first thing mentioned in the Dhammacakkappavattana Sutta: the first thing mentioned is the Middle Way, and the second thing mentioned is the Eightfold Path.
The page then gives a "contemporary definition" i.e. a list of possible English-language synonyms or translations (words). To this list of words I'd add that "stress" is another translation (some people have disagreed with whether it's a good translation). I might also suggest "dis-ease" or "uneasiness".
Antonym of sukha
I think it's worth noting that dukkha may be (may have been understood as) an antonym of sukha.
Sukha is a Sanskrit and Pali word that is often translated happiness, ease, pleasure or bliss. From the time of the earliest early scriptures, sukha is set up as a contrast to preya "pleasure", where sukha is a deep and authentic positive, fulfilling state of being that is lasting and not merely transient and ultimately unsatisfying, requiring constant modification, like preya. In the Pāli Canon, the term is used in the context of describing laic pursuits, meditative absorptions and intra-psychic phenomena.
Types of taṇhā
Given that stress and craving are related (as described in the Second Noble Truth), you might understand it further by knowing the different types of craving described in the Second Noble Truth:
And this, monks, is the noble truth of the origination of stress: the craving that makes for further becoming — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving for becoming, craving for non-becoming.
Wikipedia has a further description of the three types of craving ... and each term such as 'Vibhava-tanha' is mentioned in several posts on this site.
Types of dukkha
There is a sutta which describes "three types of dukkha".
sankhāra-dukkhatā doesn't mean, "the suffering of conditioned existence" nor "fabricated things are unsatisfactory" ... instead, what it means is that there's a type of dukkha that's fabricated.
vipariṇāma-dukkhatā doesn't mean, "anything that's impermanent is unsatisfactory" ... instead, what it means is that there's a type of dukkha that's impermanent, and/or a dukkha which re-arises because pleasure is impermanent
I'm not sure about the second of these (I suspect that other suttas say explicitly that what's impermanent is unsatisfactory) but I hope that at least the first (about sankhāra-dukkhatā) may be a useful description/insight.