I am a lesbian, and I am currently married to a woman! I love my wife very much.
Congratulations! I support equal rights for you and your wife in this country.
Thank you! I really appreciate the support. It's always nice to have allies. Same-sex marriage only became legal here in the U.S. very recently, under the supreme court decision, Obergefell v. Hodges. 
Interesting. I've heard that other countries in places like Europe passed same-sex marriage laws long before the US.
Yes, you're right! Currently, it's recognized in countries like France, Germany, Ireland, and Spain. 
Cool! I've also heard that some countries recognize it as domestic partnership. How is this different than marriage?
A domestic partnership is basically a status that applied only to same-sex couples during a time when same-sex marriage wasn't allowed. It's much like a "lite" version of marriage, in that it doesn't provide the same protections or rights as marriage does. 
That's interesting, how is marriage more protected or have more rights?