I am going to attempt here to write a full description of how Eligius pays pool contributors, including a description of both the CPPSRB system and the payment queue.  My goal is something that can be linked or copied and pasted whenever somebody comes with a question like this.  I want to cover a lot of bases and give some solid examples.  Everybody, please let me know if there are any corrections needed.

CPPSRB SYSTEM:
First, some terms.  Given the Eligius hashrate, and the Bitcoin difficulty, there is an expected number of shares before Eligius finds a block.  Let's call this number N.  A pure PPS (Proportional Payment) would immediately credit each and every share with exactly 25/N BTC.  This is called the PPS value.

Every share submitted goes into a stack.  The Eligius system refers to it as a "shelf" system, but in basic computer science terms, it is a stack.  It is a LIFO (Last-in First-Out) system, like a stack of plates in a cafeteria.  Each share is "worth" its PPS value, but it might or might not ever be credited to your balance.

Each time a share is found, the system immediately awards the top N shares in the stack, and each of them is credited with its PPS value.  In this way, it is somewhat like a PPLNS (Payment Per Last N Shares) system.  However, it differs in that once a share is awarded, it is removed from the stack permanently.  A PPLNS system will double-pay some shares some of the time (when the round is shorter than N shares, it will double-pay the more recent shares from the last round), and discard shares some of the time (when the round is longer than N shares, any shares older than N are discarded and never paid).

So let's say that N is 100 shares, i.e. we expect to find a block every 100 shares.  (I'll keep the values low here just to keep things simple.  Multiply by some billions to get the actual numbers.)  Shares are added to the top of the stack as soon as they come in.  First round, the pool finds a block at 120 shares, longer than expected.    So the most recent 100 shares are credited with their PPS value, and the first 20 shares are kept on the stack.  The next round, the shares are added to the stack as they come in.  This round, the pool finds a block at 60 shares, shorter than expected.  Since those most recent 60 shares are on top of the stack, they are credited first.  Since 60 is less than N, the next 40 shares in the stack are paid out.  This includes the 20 shares that were put there in the last block.  The next 20 shares in the stack will then be credited, from whenever they were accumulated.

So, you assume credits in your account in this way.  This is the first stage.  The next stage is the payout queue. 

PAYOUT QUEUE:
You can enter the payout queue once your account balance reaches its threshold, which can be set manually.  Once you hit your threshold, you are entered into the payout queue.  The queue is just that, a queue, not a stack.  It is generally not FIFO or LIFO like the CPPSRB system.  Instead, your position in the queue is determined solely by when you were last paid out.  If you were last paid out 36 hours ago, you will be ahead of anybody who was last paid out 35:59:59 or less recently.  So your position in the queue will change all the time, as the payout queue is reduced (when blocks are found and people are paid out) or when the queue ahead of you gets bigger (because people who have not been paid as recently, have hit their threshold and entered the queue ahead of you).

In setting your payout threshold, you have to weigh the benefits of making it long or short, relative to your hashrate.  If you set it to be paid more frequently, your payouts will be very inconsistent as there will constantly be people jumping the queue ahead of you as they hit their thresholds.  It can be quite discouraging to be close to the front of the payout queue, and then for some whale to hit their threshold and their payments will be 150BTC or something, consuming the next 6 blocks and putting you 6 blocks further back in the queue.  On the other hand, if your threshold is set high, so that you are paid out (say) once a week, you will generally be at or near the very front of the queue every time you hit your threshold.  It seems that the typical choice is to set it to pay out approximately once every day, or 24 hours. 

It is important to note that as your unpaid balance grows, the amount that you will receive in your next payout grows as well.  Just because you hit your threshold doesn't mean the system stops crediting your shares; and the system will pay out the full owed amount (as of the previous block) whenever you come up to the front of the queue.  So say have your threshold set to pay you out roughly every 24 hours, which is equal to ~0.1 BTC given your hashrate.  Somehow there is a backlog in the queue, and you don't actually get paid for 48 hours.  When that payout occurs, you will be paid out ~0.2 BTC.  The next time, it takes 36 hours for you to make your way to the front of the queue, so you are paid out ~.15 BTC.  So your payment per mining hour will be consistent, but the payments might be inconsistently spaced.

Payouts are typically handled in the coinbase transaction when the block is mined.  This means that the coins are mined directly to your mining address, and the pool never holds the coins in its wallet addresses.  However, sometimes something gets screwed up, and the CPPSRB system goes into failsafe mode, and all mined coins are sent into Eligius's cold wallet until they are paid out in a manual payout by wizkid057.