These two analogies refer to immigrants and to how the immigrants assimilate. The idea of the melting pot is that immigrants meld their values, traditions and other cultural aspects with the home country's culture. Therefore there is a sharing back and forth of ideas. The country takes from other's ideas and cultures just as the immigrants take from their new home country's culture.
A salad bowl analogy means that although people in the country, of all different backgrounds, mix with each other and maybe even take on the flavor (metaphorically) of each other's cultures, the people ultimately retain their own culture first. There is less of a sharing and becoming all the same than in the melting pot.
There is a big argument about which one is better for the country: do we want everyone to have one culture and one national identity or do we like the salad bowl idea where each person is valued for his or her own identity even though the people in the country are all different.