When we are looking at absorbances of solutions, we use a formula known as Beer's law (see links below). This shows a linear relationship between the concentration of a solution and the absorbance (i.e. how much light was absorbed by a sample. There are limitations to the law but it gives very good results when we are within those limitations, the key of which being that we have dilute solutions and that the solution will absorb light.
A = Elc
Where A is the absorbance, E is the molar absorptivity, l is the pathlength, and c is the concentration. Since we are given all values except the molar absorptivity, we can place the numbers in the equation and solve for the unknown.
0.689 = E* 1.00 cm*0.070 M
E = 9.84 cm^-1 M^-1
Because absorbance is one of the few unitless numbers in chemistry, we need the units of the molar absorptivity to cancel out with the units for l and c so that we are in fact left with a unitless number.