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Fluxor: Assume I bought a Bull Debit Spread for $100-$105 on stock XYZ, which was trading at $101 at the time. The total cost of the spread is $250, so my maximum theoretical profit is $250.

First, let's clean up the terminology: it's a Bull Call Spread, for which you incur a debit when setting it up. (There are also Bull Put Spreads, Bear Put Spreads, and Bear Call Spreads, and you incur credits for some, debits for others...)

Assume also, that immediately after I bought the spread, the stock price goes to $106 and stays at 106 forever.

What I don't understand is what exactly happens when I close my spread? Is somebody actually buying the spread?

Reasonable question; most likely some "market maker" is taking care of it. You can still conceptually think of a counterparty, perhaps two of them, doing the respective buying and selling as you sell-to-close and buy-to-close at your end.

Or am I just exercising the Buy part of the spread and covering it with the Sell part of the spread?
If this is the case, then I have these two additional questions:
* Why is the profit still dependent on the time to expiration? (profit keeps going up until it reaches max profit very near or at expiration).
* The stock price is already above both strike prices, so if I decide to close my spread, why don't I get the maximum profit immediately, and have to wait until the expiration is near?

The answer is in that little troublesome thing called Time Value. When the market price is above the upper leg of the spread, the Intrinsic Value is at its max, as you correctly discern. But Time Value is still present in each leg, and more so in the short leg (the one you have to buy back in the process of closing) and since it's greater than the TV in the lower leg, you won't get that max value until both TVs are nil.

The only other factor that influences the amount of Time Value (other than time itself) is the matter of how far in-the-money the spread is. As it gets deeper into the money, the TV gets smaller, reflecting the dwindling probability of the market price ever coming close.

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