Understanding values saved in WAVE file
What you see are time-domain samples that correspond to the displacement of a speaker from some rest position as a function of time. For example, the first sample corresponds to the membrane's position at $t=0$, the next represents its position at $t=T$, and so on, assuming that there are $T$ seconds between samples. Common sampling intervals for audio include $T = \frac{1}{8000}$ sec and $T = \frac{1}{44100}$ sec.

In order to turn a stream of samples into real audio, a digital-to-analog converter (DAC) is used first to generate a time-varying analog voltage that corresponds to the samples. This analog voltage would be applied to the input of a power amplifier that drives the speaker. The speaker is designed in such a way that the position of its membrane varies proportionally to the speaker's input voltage. At the end of this chain, then, you have a speaker membrane that moves in accordance with the original audio samples, producing the desired audio via its vibrations. 

As you noted, the sample values are normalized to a range of $\pm1$. The resulting loudness of the audio can be affected by many non-digital factors, such as the gain of the amplifier driving the speaker or the DAC's output voltage range. The peak sample values $\pm1$ just correspond to "maximum membrane displacement that the hardware can generate." Therefore, there is no way to encode absolute loudness of the audio in such a stream of samples, hence the use of such a normalization scheme.