How might WFIRST help us better understand dark energy? In the video linked in the Space.com article What Would It Mean for Astronomers If the WFIRST Space Telescope Is Killed?, (available in YouTube as WFIRST: The Best of Both Worlds) after 02:00 Caltech cosmologist Yun Wang says:


  WFIRST will allow us to potentially make ground-breaking discoveries, finding out what dark energy is. So this will tell us if dark energy is an unknown form of energy, or if its a modification of general relativity.


Without going too deep in to GR, how might that happen? 

Question: What kinds of WFIRST observations  and interpretations would be used to potentially address the nature of dark energy? 

Based on comments, I'll reclassify the following as an afterthought:

Is this in any way related to news about a recent observational non-exclusion of Erik Verlinde's theories (the guy who's "Trying to kill dark matter"), discussed in Margot Brouwer's 2016 video Verlindes new theory first tested with weak gravitational lensing about the VLT Survey Telescope kilo-degree survey results (see also Cosmos Magazine's New theory of ‘dark gravity’ passes first test, but Einstein’s still on top, or am I mixing apples and oranges?
The WFIRST's study of dark energy is pretty straight forward.   It's no different than the previous ways of studying dark energy.   It's not studied directly, cause we can't see it or re-create it, it's studied by the effect it has on the relative motion of distant galaxies.

WFIRST will get much more accurate readings on the relative velocity of galaxies both relative to each other in their neighborhood and relative to us, this will get a significantly more accurate estimate for dark energy than was previously possible and questions can be answered such as, is it speeding up.

NASA's WFIRST Web page discusses this in more detail


  The High Latitude Spectroscopic Survey will measure accurate distances
  and positions of a very large number of galaxies. By measuring the
  changes in the distribution of galaxies, the evolution of dark energy
  over time can be determined. The High Latitude Survey will measure the
  growth of large structure of the universe, testing theory of
  Einstein's General Relativity.
  
  Type Ia Supernovae (SNe) Survey uses type Ia SNe as "standard candles"
  to measure absolute distances. Patches of the sky are monitored to
  discover new supernovae and measure their light curves and spectra.
  Measuring the distance to and redshift of the SNe provides another
  means of measuring the evolution of dark energy over time, providing a
  cross-check with the high latitude surveys.
  
  High Latitude Imaging Survey will measure the shapes and distances of
  a very large number of galaxies and galaxy clusters. The shapes of
  very distant galaxies are distorted by the bending of light as it
  passes more nearby mass concentrations. These distortions are measured
  and used to infer the three-dimensional mass distribution in the
  Universe. This survey will determine both the evolution of dark energy
  over time as well as provide another independent measurement of the
  growth of large structure of the universe.


Dr. Yun Wang's comments appear to be written for a Science-TV show and/or youtube video, and video like those are designed for a general audience so I wouldn't analyze that particular sentences meaning too closely.

As for Erik Verlinde's . . . ideas.   I'm not a fan of his proposals, but the answer is mostly the same.   WFIRST will get more accurate readings and better readings should help get more specific answers.