Don't understand what is meant by signal dimension
In digital communication systems, the dimension of a modulation scheme refers to the number of basis function, i.e. independent/orthogonal signals (in this case $\sin$ and $\cos$ function) used to represent the symbols. In these systems $k=\log_2 M$ binary digits are mapped into analog waveforms below
$$\left\{s_m(t), m = 1, 2, \ldots, M \ \big\vert \ M = 2^k\right\}$$
Take a PAM signal for instance, this has the form
\begin{align}
s_m(t)&amp;=\Re\left[A_mg(t)\exp\left(j2\pi f_c t\right)\right]\\
&amp;= A_mg(t)\cos\left(2\pi f_c t\right)
\end{align}
One basis function (one axis), the in-phase component (here $x$-axis) is used to represent the signal. The signal is one dimensional. Now consider PSK modulation, the signal waveforms are represented as
\begin{align}
s_m(t)&amp;=\Re\bigg[g(t)\exp\left(j2\pi\frac{m - 1}{M}\right)\exp\left(j2\pi f_c t\right)\bigg]\\
&amp;= g(t)\cos\left(2\pi f_c t + 2\pi\frac{m - 1}{M}\right)
\end{align}
Which can be decomposed down into sine and cosine components. This is a two-dimensional signal. The same goes for QAM signals. 

A common misconception is taking the dimension for the number of bits per symbol. In brief, the dimension is the number of orthogonal basis functions used in the linear combination representing the waveforms $s_m (t)$. Note that despite the digital part of it, what is not always aparent is that the modulator takes in charge the mapping of the binary info into the symbols in the analog domain ready for transmission. 

Having said that, there is also a notion of multi-dimensional signals where the time and frequency intervals are subdivided into short intervals for transmission. More on this and my explanation above see $[1]$.

$[1]$, J. G. Proakis, Digital Communications, 4th edition, McGraw Hill, chapter 4.