This book has been around for many years, but as a brief introduction to the history (and people) of mathematics, it is hard to beat. The treatment of the 16th to early 20th centuries, covering solutions of the cubic and the appearance of i (square root of -1) through to the beginnings of modern abstract mathematics, could hardly be improved on in so few pages.
This book is exactly what it says - concise. If you are looking for a detailed history I would recommend Carl Boyer's rather more substantial "A History of Mathematics". However, don't be put off by this, as Struik's book is perfect if you just want an overview of the subject. I have found it particularly useful because it spends the majority of its time discussing later European Mathematics, and less time on Babylonian and Classical, which, although very interesting, don't really help the reader to understand the transformations of early practical maths into the abstract entity that we see today. The chapters vary in length, but are conveniently split into numbered sections, and thoroughly referenced. Not too much prior mathematical knowledge is needed, and there are very few actual equations, but some idea of general topics would certainly help the reader to fully appreciate the argument. Some people may find the style of writing intense, but overall I would certainly recommend this book to anyone, student or otherwise, wishing to enhance their knowledge of Mathematics and its origins.