What are pluripotent stem cells used for?
Understanding development/regeneration, generating organ(oids), creating disease models, tissue engineering.
By definition, a cell that is 'pluripotent' is one that can differentiate into any cell type. This includes cells of the ectoderm, mesoderm and endoderm. Embryonic stem cells (ESCs) are probably the only truly pluripotent cells that exist naturally. It is however possible to 'create' pluripotent stem cells by a technique known as Induced pluripotency (iPSCs) by overexpressing certain genes that are characteristic of pluripotent cells. Discovery of this technique won the Nobel Prize in Medicine in 2012.
Although out of the scope of the question, it is interesting to note that, since almost any cell can be reprogrammed to a pluripotent state, the idea that differentiation is a unidirectional process has come under question.
As for applications, it is possible to differentiate pluripotent stem cells to a desired cell type using temporal and spatial cues that can be chemical (growth factors, cytokines, other molecules) or physical (mechanical stress)
Because of this, it is possible to recapitulate developmental and regenerative processes in vitro. For example, it is possible to track what changes a stem cell must undergo to become a liver cell, or to study how the liver regenerates when cirrhosis is induced.
Directed differentiation of stem cells can also be used to create 'mini organs' in the lab, that can be used as models to test drugs and understand disease.
Tissues created in this way can also be used for transplantation. This has already been done successfully to give human patients a new urinary bladder and cure age-related macular degeneration. Studies are underway to create tissue-engineered pancreas, cartilage, bone, cornea, liver, kidney, etc but much research is required before it can be used safely and predictably for transplant in humans.
Induced pluripotent stem cells are special, because they can serve as excellent disease models and steer clear of ethical constraints of obtaining stem cells from aborted fetuses. For example, if you take a skin fibroblast from a diabetic person and generate pancreatic cells from it, this will serve as a model of a diabetic pancreas.
I realize this answer is rough. As time permits, I will work on it further to make it concise and easier to understand.