Market share is how much of the market does one business own. It doesn't get any simpler.
Lets look at the supermarket industry for example Tesco might own 23% of the market, Asda 30%, Waitrose 15% and so on. The higher the market share the more customers you have hence your are more successful.
Market growth on the other hand means an increase of demand for a particular product over a period of time. A low market growth is not always bad.