Information to be transmitted being a stochastic process?
The excerpt is intimating that, for communication applications, the information source is stochastic in the sense that its output is not fully known a priori. If you did know its output, then you wouldn't need a communication link at all! With that said, there are levels of gray to this effect, and there is a large area of study on its own known as information theory. Here's a very basic high-level summary:

The amount of information conveyed by a transmission is related to the amount of entropy contained in the transmission. Its entropy measures how unpredictable the transmission is. In your example, if a receiver observes a signal that is fully deterministic (i.e. it is completely predictable), then that transmission contains zero information. So, in a sense, the less we know what to expect about the next observed transmission, the more information that it can carry.

So, in terms of maximizing information rate, you want to maximize the entropy in your transmitted signal. However, there are some cases where reducing your transmission's entropy could be advantageous. Specifically, error-correcting codes are encoding methods that allow a receiver to recover from symbol errors by exploiting intentionally-inserted redundancy into a transmitted signal (which reduces its entropy). Thus, the information rate is lower, but the probability of error is reduced as well.