Empirical reasoning, which can also be called "inductive" reasoning, is a way of arriving at general truths about the world by making specific observations. Empirical reasoning relies on the use of first-hand observations, accumulated over an extensive period of time, in order to express general scientific principles. For example, in a very well-known case from history, the scientist Alexander Fleming, who had devoted a large portion of his early career to studying the properties of staphylococci microogranisms, one day noticed that a strange fungus had grown on his laboratory samples, and the stapylococci residues around the molds had all died. After making this observation, Fleming isolated the mold, which was from an organism of the genus Penicillium, and began to apply it to various staphylococcus samples (staphylococcus refers to a kind of microorganism that often causes bacterial infections in humans). After application to each sample, he noticed that the staphylococcus could not tolerate the presence of the mold, and was killed. By using empirical reasoning, Fleming observed the specific results of the introduction of the mold to bacterial samples to arrive at the general conclusion that this substance was toxic to microorganisms and could be used as an antibiotic. Thus, Penicillin was born.
Empirical (inductive) reasoning can be contrasted with the opposite method of scientific investigation, deductive reasoning. Deductive reasoning is the use of general principles to explain specific phenomena in nature. For example, because flat-earthers today believe the general proposition that the Earth is not a sphere, they use this general principle to explain specific observations. If a flat-earther pours a glass of water on the ground, they will use their general belief of the flatness of the Earth to justify why the water does not immediately start to roll way from them, as it would if it were poured onto a children's ball.
This is, of course, an extreme example, and the point is not to discredit deductive reasoning in favor of inductive. Deductive reasoning has extremely important implications in the study of logic and philosophy (Plato is probably the most famous deductive thinker to have ever lived). I have simply used the flat-earth example as a way to distinguish between the two modes of scientific inquiry.