Science is an activity that consists in the explanation, prediction, and control of empirical phenomena in a rational manner. By "scientific reasoning" we mean the principles of reasoning relevant to the pursuit of this activity. They include principles governing experimental design, hypothesis testing, and the interpretation of data.
Scientific reasoning is important not just for institutional scientific research. It is true that scientists use specialized theories (e.g. quantum physics) which non-scientists do not have to use in everyday life. But many of the principles of reasoning (e.g. rules for identifying causes) are applicable also to everyday life. Even if we are not scientists, we need to make use of good reasoning to explain, predict, and control the events around us. When we want to jumpstart our career, protect our investments, improve our health, we need to gather evidence to find an effective way which is likely to achieve our aims. In all these cases, good scientific thinking skills help.