If nobody ran full nodes there would be no Bitcoin, so they're important. Of course, not everyone in Bitcoin needs to run a full node for Bitcoin to work, but a healthy network has a good number of full nodes. Core developers have for some time been concerned that full node count has been low and declining. This survey seeks to provide clues why. Please take a moment to vote and comment as appropriate. Thanks!  

Edit: to clarify a full node is software that downloads the full blockchain in order to verify and forward valid blocks and transactions. Bitcoin Core is an example of such software.