If you don't understand anything that was said, here's a very simple way for you to take care of this problem.
First off, we're assuming that you just want to show your mother the pictures and that she isn't going to be printing them. Cause if she is, then she WANTS the higher resolution pics.
The easiest solution is if you have Windows XP, then you can basically download a handy resizing tool from Microsoft to handle this problem. So before emailing the pics, you'll just want to select the picture(s) you want to email, right click on them, and click on "Resize Images."
Microsoft developed some useful tools they called Power Toys that take care of common problems. Click on the website I referenced below and then scroll down to the "Image Resizer" program and download and install that. Once you do, this adds a handy new command in the menu that you get when you right-click on an image file. That new command is called "Resize Pictures." Once you select this command, a new box will ask you what size you want to resize the pics. There are several popular sizes you can choose from, or simply specify what custom size you want to send it.
If you are just emailing them so that she can see them, I'd choose a simple preset size of like 800x600. The files will then be resized and then saved as a new file in that folder (or replace the existing file if you tell it to). So if you resized a file called IMG_0001.JPG, the new file will be called IMG_0001 (medium).JPG or something similar so that you still know what file it is and what size it resized it to.
Then simply email these new files instead. Since they are smaller in size, they'll show up just fine on her computer.
That is, by far, the easiest and fastest way to resize pictures since you can select multiple files at one time and hit the resize command only once and have them all resized.
But if you don't have Windows XP, then you'll have to use some kind of image editing program and you'll have to find where you can either "Save for Web" like others said, or find where you can manually resize and image (again, 800x600 would be a good setting) and then save.
Once you do, all you have to when resizing the image is right-click on the file.