This is an excellent question. I always like to go back to the Greeks because they are one of our first sources of literature in myths, plays, and philosophy. It is my belief that many of the ideas that we have today, even, can be traced through time back to Sophocles, Plato, or Aristotle. Furthermore, there is a school of thought that there are no new ideas; every idea ever thought was thought during Ancient Greece and other such ancient times.
In terms of the influence it's had on my understanding of literature, it's helped me see characters and their relationships on a deeper level. A specific example would be Antigone or Medea who shine light on strong women in a culture where men were considered to be the stronger sex as well as show true grief in a very relatable, agonizing ways for even me as just a reader. The philosophies I've read have taught me to look at the deeper level of what the author is really trying to say in the stories.
The main thing it has done opened my eyes and my mind to deeper messages that I might not have noticed before. I would encourage you to read the classics just to get a new perspective on more contemporary works.