Q:

What exactly is "signal swing"?

I've been seeing this term in many of the homework problems for circuits but there weren't any definition given for it in the book nor wiki. My assumption is that it relates to Vpp but I want to be certain. I would really appreciate it if someone could explain what it means.

A:

"Signal swing" simply refers to the excursions of its value in time.  The units of this value can be voltage, or current, or frequency, etc., depending on the nature of the signal.  
So if you have a signal that is a sine wave with amplitude of 1, you'd say that it "swings" to 1 and -1.  If this sine wave was being clipped because of the nature of the system around it, then you'd say that the swing of the signal is being limited/clipped.

A:

Signal swing refers to the range of values a signal may adopt. Its normal use is to allow you to determine if a circuit works as intended : for example, to determine the supply voltage you need, or the maximum input voltage a circuit will accept if its supply voltage is fixed.
For example you might be asked for an amplifier for an input voltage up to 1Vrms and a gain of 10. The input signal swing is then +/- sqrt(2) * 1V, or +/-1.4V, or 2.8V p-p.
The desired output signal swing is this range * gain, or +/-14V peak.
A first attempt at designing the amplifier might use a 741 op-amp and +/-15V supplies. This will fail at the maximum input signal level, because the output signal swing (page 3 of the data sheet) is only guaranteed to +/-12V, or even less if the load is less than 10 kilohms.
Three ways of fixing the design are:

increasing the supply voltage to +/-20V; 
changing to a newer opamp with a signal swing closer to the supply rails (a so-called "rail to rail" opamp)
changing the specification to what the amplifier can actually do (either reducing the maximum permitted input level to 0.8Vrms, or reducing the gain to 8). 

The last of these is not necessarily cheating : because the former two may increase cost, it may be your customer's preferred option, if he was over conservative in the original specification.

