Gravitational lensing is a physical phenomenon which describes light deflection by gravity. It causes distortion to images of galaxies, since the emitted light beams are perturbed before arriving at an observer. When the distortion is weak (as it is usually), we call it weak lensing.
The distortion pattern and its amplitude are directly related to the matter distribution of the Universe. Therefore, cosmologists measure the shapes of galaxies to derive cosmological parameters. This helps shaping our knowledge about the Universe.
Cosmologists use cosmic shear to extract information from shape distortion. It uses two-point correlation functions of galaxy shapes to summarize statistics on the matter distribution.
However, meaningful information will not be accessible if undesired astrophysical features and inevitable observational systematics are not properly dealt with, which demands considerable efforts.