Hands down, I would have to say that the best book on Indian philosophy, both in terms of substantial philosophical content, but also in intellectual and actual history, would be Classical Indian Philosophy by J.N. Mohanty. The author is phenomenal in both approach and in the way he provides a simplified explanation of complex and obscenely abstract notions. I also had the fortune to audit a metaphysics class of his. Interestingly enough, he is also one of the predominant scholars in the US on phenomenology as well. The guy is simply great, like an Indian Yoda.

Just to give you a preview of the book, the first section gives you a basic overview of Indian philosophical history, as well as a crash course in Vedic, naturalistic, and skeptical schools. He then dives right into the abstract parts of Indian Epistemology (parmana sastra) and metaphysics (prameya sastra). What I have really come to appreciate in the book is how definite theories like true cognition (prama) are explained and how they form a syllogistic chain from one to the other, from prama to pramanya, from perception (pratyaska) to inference (anumana). After a very thorough analysis of the metaphysics, he then goes into the more historical aspects which put the philosophy in context (which is what I would assume you would find useful since you not only want a basic descriptions of ideas, but also show the reasons as well). The two sections that deal with the contextual areas are the philosophies of law, politics, and morals (dharma sastras) as well as religion and art.

Everything is nicely compartmentalized though, so if you don't feel like looking at the philosophy first, you can skip to page 95 and start on the background first. Another thing that is invaluable is that he actually took the time to comprise a Sanskrit compendium of almost all the major terms (appn #4). A gripe I have with many Indian philosophy books is that they briefly introduce you to the Sanskrit terms and then leave it at that, or not even bother to explain it to you. Jitendra goes to great lengths to make sure you get it.

Well there is my book report for the day. LOL!