What is an idea or explanation that leads to scientific investigation called?

A hypothesis, in essence, is some random thing some random person comes up with, and using the scientific method, carries out experiments to test the validity of their hypothesis. If a hypothesis is tested valid, it's either a result of existing physical laws, or if not, sometimes a law or theory can be improved by results from the experiments.

Once a person tests their hypothesis and finds it to be valid, they can then develop a theory based on their data conclusions and results. Once a theory becomes readily accepted from the scientific community, it can become a law or a principle. Some theories are both true and false, but still not be invalidated. For example, Newton's theory that all objects fall at the same velocity wasn't wrong; it was just incomplete; i.e. it had a range of validity. Air resistance and terminal speeds, as well as relativistic effects (which Einstein tested) provide a more complete view on the effect of gravity on objects.

A theory is an explanation of why something occurs. If the explanation is correct the theory should make correct predictions about what will happen.

The prediction is called a hypothesis. The Hypothesis is a statement about what will happen in the experiment. If the Hypothesis comes true it provides support for the theory, If the Hypothesis does not come true it brings the theory into question.

Einstein made a prediction based on his theory of relativity that the light would be bent by a gravitational field. He even calculated the degree of bending. His theory said that gravity would slow down the time experienced by the light causing the light to bend.

The idea that time was relative and could change seemed outrageous to the people of his time. The prediction was tested during a total eclipse of the sun. To peoples amazement Einstein's prediction were correct. That his hypothesis based on his theory was proven correct by the experimental evidence caused his theory to be accepted. ( Note many scientists even today fail to take into account the concept that time is not constant in the universe)

Einsteins theory of gravity did not contradict Newton's laws of gravity. Laws describe what will (always) happen but not why. Theories explain why what happens. Theories are tested by Hypothesis that predict what will happen in an experiment.