When you paste a link into a mind map, MindMeister expands it automatically. If you're pasting a link from YouTube, the video is automatically embedded in the topic. If you're pasting a link to an image, the image will be embedded. If you're pasting a link to a website or blog, the featured image of the page will be embedded.
If you don't want links to be expanded automatically, you can turn the behavior off in your settings:
Click on your user avatar in the upper right corner of the screen and select Settings. In the new dialog that opens, switch to Advanced, and there flip the switch next to the setting 'Automatically expand links'.