One of the details that shows how seriously we take our Seder, is the matter of reclining, or הסבה in Hebrew. We are meant to follow the dictates of our sages and how they directed us in carrying out the Seder.
The Halacha is that both men and women are required to recline only when we drink the four cups of wine and the three times we eat Matza. If we do not recline, we have not fulfilled the commandment of eating Matza or drinking the wine and it must be repeated.
We lean to the left so that the קנה, windpipe, shall not come before the וושט, the food pipe, so that we don't choke.
The leaning is a symbol of our freedom to demonstrate that we appreciate that had Hashem not taken us out of Egypt, we would still be there. This may seem like an insignificant detail, but it should be observed like all Halacha.