I know you've got a lot of answers already but here's an in-depth one, hopefully it's not too much.

A shader is just a program. It can be simple or complex, but they're just programs that get run with various types of data, and then output that same data, but changed somehow (or not at all in some cases).

For example, there's vertex shaders which take in vertices (mathematical points in space) and change them to something else. So like someone else said, the game might just be putting a flat plane of water, and a vertex shader could take those points and move them up and down to create waves. That's likely not what's happening in the image, but that's just an example.

There's pixel shaders, which take in a picture and then changes it somehow. The same program is run on every pixel on that image, which gives it the name pixel shader. Things like depth of field, color correction, bloom, motion blur, and anti-aliasing can be done with pixel shaders (but don't have to be). These are also called fragment shaders (OpenGL vs. DirectX terminology).

There's other kinds of shaders, but that should be enough to explain what a "shader" is in general terms. Just a program that takes in information and transforms it into something else.

So what askthepro is saying is that Ubisoft just took some time to realize that the algorithms they came up with for Watch Dogs's water could also be applied in their other games.