While it looks like a merger of the comment by @Sawarnik (+1) and the answer by @airhuff (+1), maybe an illustration of this quasi-steady state approximation or Bodenstein principle is of benefit. A brief search on the internet yielded an excerpt of a textbook of biochemistry, made freely available Wiley-Blackwell, with these two figures and a reference to the very original works about this phenomenon:

Please note that the width of the arrow $\ce{A -> B}$ is slightly different to the one relating $\ce{B -> C}$ in left-hand figure 1.12; but not in right-hand figure 1.13. You may see this as a hint of slightly different reaction rates leading to an increase of B.
According to the author of the book, Chapman and Underhill pioneered the work (DOI: 10.1039/CT9130300496), which was expanded by the one by Bodenstein (literally "A theory of photochemical reaction rates", DOI: 10.1515/zpch-1913-0112) and still is of importance in view of biochemical reactions.
For the purpose of this post, the figures found were rearranged. The are located on page 13 (first chapter) of said Fundamentals of Enzyme Kinetics, 4th edition (2012), authored by Athel Cornish-Bowden, ISBN 978-3-527-33074-4.