The mechanism called "the cap" (3-ram capping stack, LMRP), its purpose, the dangers involved in using it, and its relation to the relief well, are included in the discussion.
The grave dangers involved are shown in Figure 3, taken from the first post in this series.
The danger in allowing the pressure to rise within the well casing is that it will breach then leak oil / gas into the strata of the sea floor around the well bore and well casing.
It could then leak profusely into the gulf waters with no end in sight unless the relief well works.
The uncertainty of the test is that it is not known how completely the well casing has held up nor how deep any damage done to it may be located.
What is known is that the relief well must come into contact with the well casing safely below any breaches in the well casing, if the gusher is to be shut off.
According to BP, a leak was discovered at "the choke" (part of the cap assembly evidently) which they are repairing prior to initiating the cap test.
Adding more mystery to all this, I found a very interesting comment over at a blog I read from time to time.
The blogger was talking about how Secretary of Energy Chu had helped out, for example recommending that BP use a gamma ray "camera" to look at the internal condition of the BOP, so BP did so:
... it told engineers which valves and rams inside the BOP were closed and which were open, and it showed that a piece of drill pipe was stuck inside the BOP.(The Oil Drum, emphasis added). I added the bold because that really caught my eye and my curiosity, seeing as how there aren't many ways a piece of drill pipe can get into the BOP.
It either happened while the BOP was being fabricated, shipped, installed, or during the explosion.
The more likely scenario is that it happened during the explosion and sinking of the Deepwater Horizon.
That is yet another reason why the suspicions that there is a breach in the well casing are valid.
Add to that the fact that both the "top kill" and the "junk shot" attempt to plug the well did not work, and one can see the reason for concern of a well casing breach down out of sight.
UPDATE: After 85 days, 16 hours and 25 minutes from the first report on April 20 of an explosion on the Deepwater Horizon, after the death of 11 workers, after some 94 - 184 million gallons of toxins spilled into the Gulf, after vast destruction to the environment, the test is underway to see if the cap holds for 48 hours. Hold baby hold!