In the most general sense, the term 'abuse' describes a particular type of relationship between two things. An abusive relationship is one where one thing mistreats or misuses another thing. The important words in this definition are "mistreat" and "misuse"; they imply that there is a standard that describes how things should be treated and used, and that an abuser has violated that standard.
For the most part, only human beings are capable of being abusive, because only human beings are capable of understanding how things should be treated in the first place and then violating that standard anyway. Animals in nature, and nature itself may be very violent and destructive at times but in an unconscious, irresponsible sort of way; they cannot act otherwise. Natural violence is not intentional, but all too often, human violence is.
Various types of abuse are possible, including self-abuse and abuse of others. From a practical and social point of view, abuse that harms other people or animals is worse than self-abuse. If people want to abuse themselves or some inanimate thing they own, they mostly harm themselves. If, however, they choose to abuse a being (a person or animal which can feel pain) in a similar manner, they end up harming that being. This is a very bad thing for several reasons: first because it harms that other being, and second because it violates a 'social contract' based on a common understanding, drawn from various religious, ethical and enlightened government principles and traditions, that hold out the idea that human beings are not things to be owned, but rather beings having innate rights and worth as independent creatures who are all roughly equal (under God). Such standards help protect people from arbitrary abuse from people who are more powerful then they are. If it is okay for a strong person to abuse a relatively weaker one "just because," then it is equally okay for an even stronger person to abuse that abuser. There would be no end to the violence under such a scenario. By insisting on the relative equality and rights of all beings (even for owned animals to some limited extent), no one being has the right to abuse another, and abusive violence is minimized. This 'social contract' is an important part of the basis of civilization itself.
Abusive actions one person makes towards another are generally intended to control the victim, or to make the victim submit to the power of that abuser. Such actions are abusive, because it is against the notion of equality of human worth to say that one person should be able to control another against the victim's will.
Keeping these definitions in mind, some actions are easy to identify as abusive, and some are not. For instance, it seems safe enough to say that a spouse should never strike his or her spouse, or put him or her down verbally; such actions are always abusive. It is also easy enough to say that all instances of forced sexual behavior (particularly where children are involved) are abusive, and that neglect of children and dependent elder's well-being is abusive.
It is harder to define abuse in other circumstances, however. It is a parent's duty to teach their children how to behave properly; to not do so would be neglectful. It is highly controversial whether corporal punishment (striking children) is an acceptable method for disciplining children. It doesn't seem reasonable to say that all instances of corporal punishment are always abusive. Some parents who use corporal punishment may do so for very legitimate reasons and under appropriate circumstances. However, it is equally clear that some parents do cross the line into true abusiveness with their corporal punishment practices. Seeking out the consensus opinion of respected others in the local community and the nation is probably the best means of determining whether an ambiguously abusive action is abusive or not.
There are individual difference between people in terms of their comfort level with 'abusive' behaviors as well. For example, some couples are very volatile with one another; they may scream and yell at each other and fight constantly. Being subjected to this high-conflict sort of relationship might be an instance of verbal abuse for some more sensitive people. However, if both partners in a high-conflict marriage are adjusted to that high level of conflict and are okay with it, then their fighting may not actually be abusive at all as applied to their individual situation. Similarly, people who willingly and consensually practice sexual bondage in the context of their intimate relationship are not engaging in abusive behavior, until and unless one partner uses it against the will of the other partner. The important take home lesson here is to note that when it is not clear whether a particular behavior is abusive or not, it is best to fall back on whether that behavior feels abusive or not. If it feels abusive, it is likely to be abusive, at least for you, and in any case, you would be justified in escaping from that abuse. However, the same behavior might not be abusive for another person.