The basics: The Indigo Girls are Amy Ray and Emily Saliers. Amy is the more intense, low-voiced, rough-edged, rock n rolling brunette. Emily is the more lighthearted, high-voiced, folky, blonde. They never write songs together, except for two songs: "Blood Quantum" from Honor, which is a benefit for the Honor the Earth Campaign, and a dirty, funny song called "I Wanna Be Your Lover", which can be heard on the relatively common bootleg Blue Food. (The Indigo Girls don't mind bootlegs as long as they are traded freely, not sold.) They emerged from the Atlanta, Georgia music scene, having known each other in grade school and ended up at the same college. Aside from music, they focus their energy on environmentalism, the rights of indigenous peoples, and gay rights. For answers to more IG questions you can consult the FAQ list.
I would rhapsodize about them further, but it's been done. :) It'd probably be best if you went to their official website, which has sound and video clips and other fun things. You can also join the ridiculously-high-volume mailing list, which I had to unsubscribe from because I was going over quota on my email account every other day. But the mailing list people are great, and it's a good place to start a collection of boots. And you can check out the Lifeblood site for lyrics and zillions of articles about them, and a good fan site for general worship and an index of all things Indigo. You also might want to check out Daemon Records, Amy Ray's not-for-profit independent record label, and The Honor The Earth Campaign, a grassroots Native American and environmental group.
You can also garner info from online record store CDNow, but it's probably better to support your local, non-chain-owned record store with your purchases!