What it is
Helplessness is the inability to affect what is happening. It is a frequent element in much of BDSM and is closely related to the disparity of power upon which BDSM is based. While the disparity is usually that one person (the top, dominant or master) has more power in a particular situation than their partner (the bottom, submissive or slave), helplessness is the extreme where the bottom, submissive or slave has no power.
Importantly, the existence of a difference in power between the partners involved is not enough for BDSM to work. The difference needs to be actualised for it to be experienced and for it to have the opportunity to be satisfying, rewarding and productive. This means that the difference in power must be used. A dominant must command his submissive, or must take control and use him or her. Merely being in charge does nothing until you do things with this power, give directions, use the power to make things happen, etc.
Creating the feeling of helplessness
Creating the feeling of helplessness is one way that a dominant can activate this difference in power. Very commonly it involves bondage, cages, mummification or some other form of restraint. The actual restraint though is not enough to create the feeling of helplessness. Once tied up a person can be made to feel helpless by subjecting them to something which they cannot usefully resist. This could be, for example, nipple torture, tickling, torture or teasing.
Physically restraining someone is not the only way to create a situation of helplessness for them. Taking advantage of powerful drives in them which only you can satisfy is another way of exploiting and making them feel helpless. These can be sexual drives, hunger for pain or for submission, need for surrender, and so on.
Whipping someone into an erotic frenzy, for example, is a good way to create feelings of helplessness. Someone who is at your mercy at the end of your whip as you target their pink bits is going to feel intense sexual hunger which only you can satisfy at your whim. You can manipulate this to build the feeling of helplessness until they know that you are the only one who can release them from the hunger.
Almost by definition, a submissive needs to submit or to surrender. But to do this, to achieve their desired state of mind or to achieve subspace, they need a partner to create the circumstances for it to happen. While it's usually a completely internal hunger which their partner is not directly able to influence, the partner can provide an outlet for it and this outlet will be what the submissive will be hungering for. Their dominant can manipulate how much or how little of their "submission" their partner can express, and this allowing and then holding back by the dominant can illuminate to the submissive how helpless they are.
A service-oriented submissive can also feel helplessness when their partner removes the opportunities for them to serve. Someone whose involvement with their partner revolves around being useful, in attending to their partner's needs, in providing personal service or making their partner's life easier will feel helpless if their partner starts doing things for themselves. This can be an effective form of punishment.
Helplessness and surrender
Finally, helplessness is tied to surrender. Surrender is a powerful, often intense, human experience and the fact of having no power, of being completely helpless, and yielding to it creates a strong internal release or change which may be highly desirable.