If you insert correctly an image with the right format (.jpg, .png or .gif) in your content editor and it still doesn't show in your message, that happens probably because of spaces in the name given to that image. Eliminate the spaces and the image should be visible (e.g.: From "My Image.jpg" to "MyImage.jpg" or "My_Image.jpg").
Another explanation would be that the name of the image is very long. Shortening it will help the content editor to upload the image more effectively.
Note about copy/pasted images: If you copied the image from another source and pasted it in your editor, it is saved as a temporary file on your computer with a name consisting of a long string of characters. This will make it visible on your computer, but it won’t be seen by your clients on their computers. So, make sure that you use the “Upload” feature when inserting images.