Wages are how much you pay your government employees per day, including those employed at the ground defenses. The government wages define the standard for the colony. Paying your people higher wages than the universal average wealth improves many aspects of colony life, it lowers crime, sickness, and improves happiness. However, wages are only as effective as the amount of people they affect and only up to a certain point.
This means that changing wages on a colony that has less than a percent of your people employed in government jobs will likely not seem to do anything.

Any wages you pay are fed into the wealth of the colony, meaning higher wages means higher wealth and lower wages is lower wealth. Low wealth can be very dangerous so paying your people enough is essential to keeping your colony stable.
High wages, especially on colonies where you employ a massive portion of your population, is also dangerous. Your colony might be happy but it will drain your funds making the colony a financial liability. So make sure you find the right balance between colony stability and profitability.

The average wages across all your colonies also serve to determine the personnel cost of your ship's crews.

Please note, that scientist's salaries do not factor into regular wages.