Composer Richard Rogers—along with his lyricist partners Lorenz Hart and, later, Oscar Hammerstein II—helped to change American musical theater from a more frivolous type of entertainment to a more serious and realistic artistic performance. His music is considered classic with over 80 standards that are still performed today, such as My Funny Valentine, which has been covered by more than 600 artists. He won multiple awards, including a Pulitzer Prize. His catalog is enormous, and summarizing his work in two pages will not be easy.
One thing that jumps out is how well his Broadway musicals transitioned to film, which doesn't always happen. You might explore the reasons why, such as how well he and his partners captured the zeitgeist of the moment. You could also explore how timeless their work is, since musicals and films such as Oklahoma! and My Fair Lady are still being performed and enjoyed worldwide today. His music has been described as "wonderfully singable, danceable melodies" but he also wrote darker, more longing and wistful tunes as well.
Rodgers himself is quoted as asking "What is wrong with sweetness and light?" In short, these are popular and catchy tunes that score well and provide opportunities for the vocal and dance showcases that made musical films so popular in their day. The bottom line is that the public was and is able to relate to the melodies he composed, which has contributed to Rodgers' continuing success and acclaim.