Market segments are a way of splitting up the market in the relevant segment (which differ per industry). So for example in the automotive industry you might split it up by car-type: small, medium, sedan, SUV,..
Customer segments focus on the specific characteristics of customers, which could be age, income etc..
For this example, you can use market and customer segments to better understand what it going on vs if you would focus on the general trends. Looking at the SUV sales for each age bucket can reveal important trends (e.g. SUVs are becoming more popular under 21-30 year olds).
Hope this helps!