This is a useful if well-hidden feature, in OpenOffice Draw and Impress.
Let's say you've got some lovely graphics for your business, and you're going to put them on your web site.

So you add the logo, the first one, to your web page. But! Hey, what's up with that? There's a white background that didn't show up before. And you're not about to change the pink background.
So to get rid of the white background, here's what you do.
1. Create a new Draw document and insert the graphic. (File > New > Drawing, then choose Insert > Picture > From File and find your graphic.
2. To see things better, put a colored object behind the graphic, or make the background colored. To change the background, choose Format > Page, Background tab, and instead of None, select Color from the list. Select any color and click OK.
3. Choose Tools > Eyedropper.
4. Click on the graphic. Then click in the first checkbox on the left.

White is the default source color. However, if there's a different background color, or just to practice, you can then move your mouse over the white part of the graphic and click on it to select the color you want to get rid of.
5. Select Transparent in the corresponding dropdown list on the right. Again, this is the default.
6. Click Replace. The white will be replaced by Transparent.
7. If you didn't get rid of enough white, increase the tolerance to 20% and try again. Keep going as necessary; sometimes you need to do 50% or more, up to 99%.
8. Select the graphic and choose File > Export. Select the format you want: PNG, JPG, etc. Click Export, and enter any additional options if prompted.
Now you can insert the new picture wherever you need it.
Now, what happens with other pictures, when you try to replace one color with another color? It all depends on the picture. Here's what happens when I replace a light lavendar with a darker lavendar in the cupcake graphic. The following illustration shows before and after. It works better if you have something very structured where there are no gradations of colors.