Imagine having some of the largest, most influential Twitter accounts sharing your content - giving you the same massive reach as they have. Even if you just have a few hundred followers, your tweets will end up in front of tens of thousands.
The phrase was recently coined by Jack Butcher, after a conversation with Matthew Kobach. In its original meaning, it is a way to "catch the attention" of someone you admire.
You do this by "becoming their intern" by re-working their original content and presenting it to your audience.