Being dominant is about exercising influence or control. Governing matters; being in charge. Predisposed to taking over and wanting to maintain power.
This term can be associated with being on the giving or controlling end of bondage, discipline or sadism but a dominant's activities might not include any of these.
The term dominant as a noun is mostly synonymous with Dom but some people use it more widely to denote anyone disposed to be dominant and would therefore say that a dominant might be a Top, a Dom or a Master.
Note that some partners like to switch roles from one encounter to the other, or even during a single encounter, depending on mood and preference. See switch.
A dominant person enjoys being in control of a submissive person. Reasons for this are said to include demonstrating skill and power, having ownership of another person, and being the object of affection and devotion. Domination may be the way in which the dominant feels most comfortable expressing and/or receiving affection. Service oriented dominants would add that it is obviously useful to have the resources and abilities of another human at their disposal.
There may be other motives, including pleasure taken not only in sheer power but in the suffering of others, thrill seeking in taking risks and outright self destructiveness. That is why many in the BDSM community are concerned with establishing the motivations of those involved in an encounter and advise caution in making BDSM connections.