In the context of BDSM, "aftercare" refers to the attention of an affectionate and caring nature that should take place after a scene.
BDSM relationships frequently push the boundaries of the participants' limits--physically, mentally, and emotionally--and in the process of this "push", a participant may feel overexposed or intoxicated. When in this state of mind, he or she is unable to think or rationalize as clearly as usual and may even have trouble differentiating between a good idea and a bad idea, fantasy and reality, or even past and present.
In any case, this kind of exposure necessarily requires a period of time after the scene during which participants can communicate about it and generally reassure one another if feeling shaky. This often takes the form of holding one another, kissing, or the best-held-together participant (often, but not always, the dominant or top) bringing water and other restoratives to the one needing more time to recover. In a scene in which a participant gives up control to another, it is imperative that the one in control ensure that there is both enough time for aftercare and a suitable place for it. Also, certain scenes involve more extreme physical sensations and activities such as piercing, cutting, abrasion, or branding, all of which require proper cleaning and protection of the affected area after the scene in order to ensure good healing. Failure to ensure adequate aftercare, as well as putting someone at risk of infection or other physical problems, can lead to the other parter feeling lost, abandoned, or otherwise distraught, and generally not very happy with the world--or his or her partner.
In a more ordinary relationship context, aftercare refers to the attention and care needed after one partner gives the other bad news or another similar shock. The easiest example of this would be in the case of an unforeseen but non-malicious breakup; aftercare in this case would be the partner doing the breaking up being there to help the other partner deal with the shock of the breakup and the resulting negative feelings that would arise from it. It is recommended that you do not break up with your soon-to-be-ex-partner's e-mail inbox or answering machine if you wish to remain friends afterwards, as not being there to help him or her through the grieving process may lead to feelings of anger and abandonment, among others. Aftercare takes place more rarely in breakups than in BDSM, however, due to the larger tendency of breakups to involve bitter or otherwise negative feelings on the parts of both partners involved.