It would be helpful if you could post the entire sentence or paragaph where the phrase is being used so I can be sure I am giving you the right meaning. "broader-based market share" should mean that the portion of the market that is buying a product or service is spread out more evenly among different groups. For example, let's say you sell a style of mobile phone that only 12-15 year old girls like. Then your market share has a narrow base. But if you sell a style of phone that both men and women of all age groups like, then you have a broad base.