The Gemara (Pesahim 120a) discusses the idea of women leaning and the early Poskim give different reasons as to why women may be exempt. The Rashbam (Pesahim 108a, sv. “Isha”) explains that a woman’s awe and subservience to her husband would exempt her from Haseva. The Sheiltot writes that it is not the nature of women to lean, while the Ran explains that a woman serves her husband and thus she is not fully free.
Rabbi Moshe Karp (Hilchot Hag BeHag) writes that women nowadays are not considered subordinate to their husbands as they were in generations past, and thus they too can express their freedom by leaning. Furthermore, many families hire help, which would allow women to more fully participate in the Seder, including leaning. Rabbi Haim Benveniste (Pesah Me’uvin, § 3), Rabbi Ben Zion Abba Shaul (Or LeZion, vol. III , ch. 15), Rabbi Ovadiah Yosef (Hazon Ovadiah Pesach) and other rabbis concur with this approach.
One practical difference between men and women is if one forgot to lean when drinking wine or eating Matza. If a man does so, he does not fulfill his obligation and must go back and repeat the Mitzvah while leaning. However, since the Shulhan Aruch says that women are exempt from leaning and the original custom was as such, it appears that a woman would not have to repeat the glass of wine or Matza if she forgot to lean, and would have fulfilled her obligation Bediavad (ex post facto).
Summary: Nowadays, women should lean at the appropriate times during the Seder. A women does not have to go back and drink another glass of wine or eat Matzah while leaning if she forgot to lean the first time.