Simplify it like this:
T-cell: very effective at killing; not as good at recognizing specific things.
Antibodies: not that effective at killing; excellent at specifically recognizing things.
CAR-T: Let's stick an antibody against X (eg CD19, CD22) to a T-cell surface so it can recognize with the antibody and kill with its innate capacity to kill.
Ta da!
It's fascinating, it is changing hematologic oncology. The bad news is, as always, the price and the manufacturing time (2-8 weeks). This last part seems to be getting better.