The equal loudness contours represent the level that different frequencies need to have in order to be perceived as having equal loudness. These curves are measured at different perceived loudness levels (phones). Phones are the same as dB SPLs for 1000 Hz, whereas for other frequencies we'll need to apply gain or attenuation for the ear to perceive the different frequencies as being equal in level.
At low listening levels, the ear has a hard time hearing very low frequencies, and, to a lesser extent, high frequencies as well. As we go up in level, the differences between frequencies even out. We could say the ear's frequency response is "flatter" at high levels than at lower ones. For example, a 50 Hz 60 dB SPL sinewave will be perceived as being some 10 dB lower than a 1000 Hz sinewave with the same SPL. However, a 50 Hz 100 dB sinewave will only be perceived as being some 10 dB lower than a 1000 Hz one of the same SPL.
The psycoacoustical phenomena of the different sensitivity of the ear to different frequencies and the variation of that "frequency response" (in fact, the contours are like frequency responses of the ear upside down) with changing listening levels was first thoroughly quantified by researchers Fletcher & Munson in the 1930s. Thus, this type of curves are commonly referred to as Fletcher & Munson contours, although these days more up to date and accurate versions are used, such as those by Robertson & Dadson (shown below), or the standards organization ISO.
Based on this type of contours are the A, B and C frequency weightings, which correspond to low, mid and high listening levels, respectively, and are used to better correlate microphone level readings with human perception.