Reputation is a measure of your standing mostly with the mission giving groups of Ascii Sector. To see what your current reputation is activate your Quine 5000, go to Stats and then to Reputation. Groups that are effected by your Reputation:
The better your reputation, the more lucrative/difficult missions are unlocked. In the case of wingmen, with low reputation only a few will ever show up, and those will not have great ships. Once you gain reputation, their number in bars will increase and their ships will get bigger and stronger.
At the start, the player will have no reputation with anyone. You can increase your reputation by successfully completing missions for the for the different factions. Failing missions e.g. by missing the deadline decreases it exponentially i.e. the more missions you fail, the higher the decrease in reputation gets.