There are three arcs running through the two volumes, but as always the most important is the middle one. The first deals with a creepy man who eats humans and has a jewel shard. Inuyasha also has to deal with the new moon when he turns human. This was developed into an episode (two actually) but set later in the series so they could go straight to Sango.
The second arc concerns Sango, an amazing demon hunter who is manipulated by Naraku into going after Inuyasha after her village is destroyed. She realizes that it was actually Naraku, but not soon enough to go after him. She also reveals a bit of the history of the Shikon Jewel, aka the Jewel of Four Souls which was created by Midoriko, a priestess who could purify each of the four souls, which I think was animal, demon, plant, and rock. She perished after a long battle against a demon (who had previously been a man who wanted her and took many demons into his body like Onigumo) in which she took his soul into hers, fusing them and expelling them which created the jewel. Supposedly Midoriko and the demon remain imprisoned in the jewel and have battled ever since.
The final arc (which actually doesn't end in this volume) is a one off story about a lake demon. It's nice to have the group together though.