The thread pool is designed to reduce context switching among your threads. Consider a process that has several components running. Each of those components could be creating worker threads. The more threads in your process, the more time is wasted on context switching.
Now, if each of those components were queuing items to the thread pool, you would have a lot less context switching overhead.
The thread pool is designed to maximize the work being done across your CPUs (or CPU cores). That is why, by default, the thread pool spins up multiple threads per processor.
There are some situations where you would not want to use the thread pool. If you are waiting on I/O, or waiting on an event, etc then you tie up that thread pool thread and it can't be used by anyone else. Same idea applies to long running tasks, though what constitutes a long running task is subjective.
Pax Diablo makes a good point as well. Spinning up threads is not free. It takes time and they consume additional memory for their stack space. The thread pool will re-use threads to amortize this cost.
Note: you asked about using a thread pool thread to download data or perform disk I/O. You should not use a thread pool thread for this (for the reasons I outlined above). Instead use asynchronous I/O (aka the BeginXX and EndXX methods). For a FileStream that would be BeginRead and EndRead. For an HttpWebRequest that would be BeginGetResponse and EndGetResponse. They are more complicated to use, but they are the proper way to perform multi-threaded I/O.