In the early years of the printing press illustrations used to be woodcuts. The image would be cut along the grain with both the text and the illustration cut from the same piece of wood. These are known as block-books. Then, as moveable type emerged, images would be cut from separate blocks and inserted where needed. This was great because illustrations could be used for multiple projects, or an embellishment used multiple times in the same book without it having to be cut multiple times. The only problem with woodcuts was that they tended to be a bit crude as the wood could not be cut very fine. Illustrations then began to be engraved or etched onto copper which allowed greater detail. With woodcuts you cut away the dead space and leave raised the area you wish to print. This is known as relief printing. The raised areas are inked and then pressed down onto the paper, like with potato printing.
For copper you either engrave or etch away with acid the areas you want to print. Ink is added to the etched areas and wiped away from the raised. When in the press much higher pressure is exerted in order to push the ink onto the paper. This is known as intaglio.
The two methods are not compatible and so need to be printed on different presses. You could perhaps print the text using one press and then later add the image to another part of the page using another press, but in reality what happened was that images would be printed on their own separate page. This was often on a different type of paper that was either more compatible to the printing technique, or just more luxurious because less sheets were needed and if you're going to spring for something, then the illustrations should really be it. So from images being printed on the same page you now had separate pages of images, called plates.
At the end of the 18th century Thomas Bewick developed another technique, which we call wood engraving. It is a method of relief printing. Whereas woodcuts follow the grain of the wood, wood engraving uses the end of the wood, which is harder. This allows for a much finer image to be formed. I won't go into the further details of the two techniques, but if you want to learn more I highly recommend obtaining a copy of How to Identify Prints by Bamber Gascoigne.
What is important is that Thomas Bewick used to produce small, highly detailed images, that could be inserted easily into a page of text and (more importantly) printed at the same time as the text. That is not to say that plates died out, far from it, but publisher's were able to easily produce much more desirable images than crude wood cuts alongside text. This meant that their books were more decorated and therefore more likely to sell. Never underestimate the power of profit! A further benefit to wood engravings is that the method uses far less pressure. Traditionally a good relief printing should just kiss the paper and leave no impression other than the ink. The higher pressure exerted for copper means that it wears down quicker leading to the finer details becoming lost. Less wear = more copies = more profit.
Thomas Bewick was well known during his lifetime, in particular for his beautifully illustrated book A History of British Birds, which was very popular. Books with his engravings are very collectable today and are well worth acquiring.