Orthostatic hypotension, (from ορθώς/orthos: "right", στάση/stasi: "standing", υπο/hypo: "below", tension: "blood pressure") is a condition where someone's blood pressure falls low enough and fast enough to cause dizziness or other symptoms  when they change position (such as from lying to sitting, or from sitting to standing).
It can be a symptom of a more serious disease, but it doesn't necessarily indicate an underlying condition. Some people have lower blood pressure than others, and it can simply be an indicator of that fact, or of getting older, or of something temporary that day--or it could point to something more serious.
We can't know what's causing it, but we can deal with the symptom in the massage room in a way that helps to lower the risk of the client passing out or falling off the table.
If the client has a history of getting dizzy when getting up off the table, look for it as an issue at every future session as well.
Having the client get up slowly and in stages, and get a chance to get comfortable at each stage, is important.
Stage 1 might be turning from prone to supine, and making sure that any dizziness has lessened or gone away before sitting up.
Stage 2 might be sitting up from a prone position to resting on the table before trying to stand, and making sure than any dizziness has lessened gone away before standing. Make sure to maintain draping standards while they are sitting up so that they are not exposed.
Often, when someone passes out, they will pitch forward rather than backwards. If someone complains of dizziness while sitting on your table, you can make sure to stand close by and in front of them in order to block them from falling if they do pass out.
If you are comfortable leaving them alone for a moment sitting up--you are sure that they are not in danger of falling--you can offer to get them some water or tea or fruit juice (UPDATE 4:46 PM ET: Matpardini made the suggestion of fruit juice in the comments; it is an excellent one, and I am promoting it here.). Some clients report that this helps settle the dizziness, and it is always a nice and caring gesture in any case.
Make sure before they stand up that they are fully recovered--orthostatic hypotension can be at its greatest when rising to a standing position, and you don't want to risk their falling. You can offer your arm to help them stand, but if you do this, be careful of two things:
- If they need assistance in standing up more than they normally would, then perhaps the dizziness has not disappeared enough, and a little more time sitting would be a better option; and
- If you do use your body to assist someone in standing or moving, be very clear on positions, balance, and body mechanics. You don't want to hurt them by accidentally dropping them, and you don't want to hurt yourself by using poor body mechanics. This is actually a large enough topic that nursing assistants, for example, spend a lot of time in school learning and reviewing it, and you shouldn't attempt it unless you know what you are doing and are positive you will succeed at it.
If this is a one-time occurrence with your client, it may just be something that happened that day for no real reason, but if it is a continuing pattern, it is a good idea to recommend that your client seek the advice of their primary healthcare practitioner to find out what it means, if anything.
Did I leave anything out?
 http://en.wikipedia.org/wiki/Orthostatic_hypotension accessed 13 November 2011