In this context "extra edge" means more qualifications or experience to get what you want. For example, if you are applying for a job that requires only a Bachelors degree and you have a Masters degree, that qualification gives you an "extra edge". I hope this helps.

An 'extra edge' is an extra advantage. It definitely isn't restricted to qualifications or experience. 'extra' just means 'additional' - it is another advantage, on top of whatever you already have. A lower price could be an extra edge if you are competing to sell something. In this case, we would have to guess what it is that gives you trust and credibility. It could be the recommendation of a famous person, it could even be a well designed website. For an athlete, perhaps high-tech shoes might be the extra edge that allows them to beat their competitors.