This is about Beer's Law, also called the Beer-Lambert Law, which states that absorbance is directly proportional to concentration of the absorbing substance and path-length (the distance that light travels through the sample).

Absorbance = extinction coefficient x path-length x concentration

The constant of proportionality is the extinction coefficient. The molar absorptivity is the extinction coefficient expressed in Molar units of concentration.

The units of the molar extinction coefficient are M-1cm-1. The units of concentration are M (i.e., molar). The units of path-length are cm. When everything is multiplied together, all the units cancel. Absorbance has no units.