Meaning of "stackexchange"
Solution 1:
I believe it's a play on "Stack Overflow" (the first site in the SE network, named for a computer error message1) and "Experts Exchange" (a computer Q&A site which exemplifies many of the bad traits that the Stack Exchange engine is specifically designed to avoid).
1 As commenters have noted, it's not actually that common an error message, although people who have done any programming at all are likely to at least recognize it as an error message, even if they don't know what it means/haven't encountered it in their own work.
Solution 2:
In addition to the other answers, it may be a pun on "stock exchange".
Solution 3:
The Stack Exchange network of sites derives its name from its original site, Stack Overflow.
Stack Overflow, in turn, gets its name from a type of computer error when a computer program runs out of a type of allocated memory known as the "stack", or specifically the call stack. In very simple terms (if not oversimplified, unfortunately), this is the memory that stores the information for what's currently going on in a program. This particular name was chosen by readers of Coding Horror, the blog of one of the Stack Overflow founders.
Solution 4:
It started with the site StackOverflow, where programmers could exchange experiences and help each other. A stack overflow is an error message, common when you make a logical error in the code.
With the success of the StackOverflow site, more sites were started using the same wiki engine. The sites were connected in a form of network, so that you can use a single identity across all the sites.
So the Stack Exchange Network is a network of wiki forums for information exchange, that was started with the StackOverflow site.
Solution 5:
It is the name of the Question/Answer system you are currently using.
The name came about in this manner:
1. Stack Overflow, the original site, was named after a well-known programming error.
2. The name was modified to be Stack Exchange for the engine, where people could "exchange" questions and answers.
Beyond that, it has no special meaning, much like many other product names.