Question: Outside my house, there is a gap visible below some of my windows. I have attached pictures to make it clear, since I don't know the terminology.

The gap is about the width of my thumb. I can see the insulation easily.

Should I fill this, and if so, how?

Gallery link: [http://imgur.com/a/P3Sl6](https://imgur.com/a/P3Sl6)

![Full view](https://i.stack.imgur.com/PXuty.jpg)

![Closeup view](https://i.stack.imgur.com/In8SE.jpg)

Note: this question is different from my other question I recently asked [here](https://diy.stackexchange.com/q/51426/14069). This is specifically dealing with the windows, whereas the other question simply involves some decorative trim.

Answer: 
Backer rod and sealant can fill the joint. Provided the installation prevents bulk water infiltration, it provides an additional layer of protection. If the joint currently allows the passage of water, this is a stopgap versus reinstalling the windows properly.
It looks to me like the window unit itself *(what looks to be the newer vinyl clad window)* may have been installed over the original sill and inside the frame of the original window. No telling why this may have been done other than to avoid having to deal with the interface between the old frame and siding.

Anyway it looks like insulation was shoved up between the original sill and the bottom of the inserted window unit. From what I think that I am seeing there does not look like there is any good way to cover over this crack.

It is possible that your pictures are warping my understanding. If you could add some more pictures that show a bit more detail regarding how the window is fitted to the house structure including the outside frame, wider view of the sill and maybe even a view near the upper part of the window it may be possible to offer better advice.