When RGB files are converted to CMYK for printing on a four-colour printer, colour shifts usually occur. Usually these shifts are small, but they can be a problem, especially if your project is colour-sensitive. Even if you upload a CMYK image to the internet, you may see colour shifts (Example below).
When you save your images and graphics from the internet, you should remember to convert that image to CMYK (and check that the resolution is high enough). This is because the CMYK gamut is smaller than the RGB gamut.
Gamut refers to the maximum range of colours for a colour space. RGB has a much larger gamut than CMYK and therefore there are colour shifts when converting from RGB to CMYK.