A lot of important things happen in these volumes, but I'm going to try not summarize everything.
The first arc features the return of Sesshomaru, who is one of my favorite characters. He makes an uneasy alliance with the mysterious Naraku who finally makes his apperance, wearing a baboon jacket since apparently that's his style. With Naraku's help, Sesshomaru can wield the Tetsusaiga and incapacitate Miroku's black hole hand.
To take out Miroku, Sesshomaru (or rather Jaken) released poisonous insects which when sucked in, poison the host as well. I hated these thing from the anime. Miroku goes from being useful, to almost useless anytime they show up. And they show up a lot. Well, he does give Jaken quite a beating to find out what they are before succumbing to the poison, which is funny.
Kagome proves vital in the battle as her miko powers have clearly started to manifest and her archery skills have gotten better. She's still not great, but she saves Inuyasha at a few critical times. Unfortunately, she also gets knocked around a bit, which worries Inuyasha.
So much so that at the end of the battle he steals the Shikon Jewel from her and forces her down the well, back to her own time. She finds that without the jewel, she can't travel back.
Sesshomaru also realizes that while Naraku's gifts were helpful, he doesn't want to be aligned with him. Sesshomaru is one of my favorite characters and this is when I think you can see that he isn't completely evil.
The second arc deals with Kagome being stuck at home and Inuyasha and Miroku investigating with Kaede who Naraku is. Over the course of the series the relationship between Inuyasha and Kagome grows, but this is when you can really see that they are starting to care for each other. Inuyasha sent her back because he did not want to see her get hurt, but when he never showed up in her time, she was worried that he had died.
She does make it back, proves that she is once again invaluable to the team. Naraku finally reveals himself to the group as well and tells of his past as the injured human thief who Kikyo helped. He chose to take demons into his body to create what is now called Naraku and then orchestrated the death/binding of Inuyasha and Kikyo. He had thought that Kikyo would use the jewel on herself, corrupting it, but that didn't work out when she burned herself with it.
As always, Naraku gets away using his poisonous miasma (honestly years after watching the anime, I associate the word miasma with this show).
The final arc features the return of Kikyo, who has been keeping herself alive with the souls of young women. She also tries to drag Inuyasha down to hell with her but Kagome manages to force her to stop by trying to call the bit of soul that Kikyo still holds back to her. While doing this, Inuyasha admits to Kikyo that he always thinks of her. And thus officially begins the love triangle of Kikyo, Kagome, and Inuyasha.