This is a brilliant book that conveys a beautiful, unified picture of mathematics. It is not an encyclopedic history, it is history for the sake of understanding mathematics. There is an idea behind every topic, every section makes a mathematical point, showing how the mathematical theories of today has grown inevitably from the natural problems studied by the masters of the past.
Math history textbooks of today are often enslaved by the modern curriculum, which means that they spend lots of time on the question of rigor in analysis and they feel obliged to deal with boring technicalities of the history of matrix theory and so on. This is of course the wrong way to study history. Instead, one of the great virtues of a history such as Stillwell's is that it studies mathematics the way mathematics wants to be studied, which gives a very healthy perspective on the modern customs. Again and again topics which are treated unnaturally in the usual courses are seen here in their proper setting. This makes this book a very valuable companion over the years.
Another flaw of many standard history textbooks is that they spend too much time on trivial things like elementary arithmetic, because they think it is good for aspiring teachers and, I think, because it is fashionable to deal with non-western civilisations. It gives an unsound picture of mathematics if Gauss receives as much attention as abacuses, and it makes these books useless for understanding any of the really interesting mathematics, say after 1800. Here Stillwell saves us again. The chapter on calculus is done by page 170, which is about a third of the book. A comparable point in the more mainstream book of Katz, for instance, is page 596 of my edition, which is more than two thirds into that book.
Petty details aside, the main point is the following: This is the single best book I have ever seen for truly understanding mathematics as a whole.