In this case, "draw" has the same meaning as it does in these phrases: "He drew water from a well." "They decided who won the lottery by drawing tickets out of a bowl." "He paid for the gift by drawing on his savings." "Draw" often contains the idea of "pull," as in "a horse-drawn wagon." Sometimes it means "to pull something out of a collection of things or a store of things." In this case, in your example, there was a collection of research that had already been performed, like a well full of water. There was a supply of research ready to be used. Perhaps it had been performed for some other reason. Anyway, somebody made a study that drew on that research. Like dipping water out of a well, someone dipped into a collection of research and pulled out some of it that could be used. Here are some other examples of figurative use. "Stephen Crane had never seen war. When he wrote 'The Red Badge of Courage,' he drew on his imagination." "In compiling the present collection of folk tales, I have drawn on the store of 140 tales with which I originally started, and chosen the best ones."

In the same way, you draw water from a well. When you reach out and gather information, you DRAW ON information.

Draw is a complicated word because it has so many meanings. You can Draw a game of football by the scores of each team staying level with each other. It can mean to sketch a picture. It can mean to move objects or people e.g. "the teacher drew the students into the classroom" or "He drew the chair closer". It can mean to pull an object out e.g. "She drew a card" or "He drew his gun". It can mean to attract e.g. "Their music really draws a crowd". And, in your case, it can mean to extract or take for one's use e.g. "She drew on her friend's strength" or "it draws on research from". So essentially, this example you have given means that the subject has taken information from research to help support itself.

It would mean the answer, result or conclusion relies on information from the research. If you said, "it uses information from the research." The sentence would mean essentially the same thing.