What triggers Marlin's "Click to resume..."?
To answer your question directly, this action (Click to resume...) is triggered by a buffer overflow of the Marlin firmware that is caused by the repetitive sending of M105 command by Ultimaker Cura (without checking the result).

This problem is a reported problem and fixed in the next release of Ultimaker Cura (please do note that as of posting this answer, the 3.6 Beta release is available for download). It appears to be a communication problem between Ultimaker Cura 3.4+ and 1.1.8+ versions of the Marlin firmware and has to to with polling of the temperature (M105). The link above also states it is fixed in the 3.6 release (which is the next release) as the fix has been integrated in the main code base.

This describes the problem:


  To update the temperatures in the monitor, Cura sends M105 pings every
  2 seconds. It seems that if this is done during a print without
  waiting for an OK from the printer, the serial buffer on the printer
  may still overflow eventually (causing Marlin to complain/pause).


and this describes the solution:


  During some operations, such as preheating, the printer responds to
  new commands with echo:busy. While it is busy, it does send
  temperature messages, but these are not prepended with an ok,
  because the ok is supposed to show that a command was received and
  executed. So the two patches I wrote do the following:
  
  
  the pattern matching no longer looks for ok messages, but looks for
  temperature updates (this fixes the temperature updating while the
  printer is preheating) 
  once the printer has said that it is busy, stop
  asking for temperature updates until the next ok is received (this
  prevents the serial buffer overflowing while preheating)
  




Old answer centered around the firmware (based on the text of the OP, no photo with the actual error message was added yet):

The text click to resume print cannot be found (with case insensitive search) in the latest sources of Marlin 1.1.9 down to Marlin 1.1.6. This means that you are using a different fork, an older version of Marlin or the message is not displayed as such.

The text message Resume print can be found, and is part of the message constant MSG_RESUME_PRINT

#define MSG_RESUME_PRINT                    _UxGT("Resume print")


But, this cannot be found in some sort of a concatenation using MSG_RESUME_PRINT!