Research, broadly speaking, is the process of gathering and analyzing data to answer problems, understand a concept, or discover something. It is something done that can solve an existing problem, understand and explore an idea, and/or make arguments grounded on facts. In science and scientific research, there are two broad categories: applied or basic.
Basic research refers to the kind of research that primarily aims to understand a concept. It involves experimentation and analysis of data obtained from experiments involving the understanding of mechanism and working of certain things. For instance, understanding the mechanism by which DNA is replicated is considered basic research - or basic science. In short, it aims to understand the fundamentals of a discipline.
Applied research refers to the kind of research that has direct effects to human life. The main thrust of applied research is the progress and development of technologies that will make life easier. For instance, drug discovery researches and research involving engineering are considered research.
In brief, basic research contributed to the increase of knowledge, while applied research aims to solve a given problem. These research categories, however, are in no way exclusive. Most scientists are involved in both. Understanding how two proteins interact with each other is considered a basic form of research. Creating drugs that will interfere with these two proteins - like those involved in cancer - can be considered applied research as it solves the problem of cancer. It can also be referred to as translational research - bridging the basic sciences and the applied sciences.
Aside from these broad categories, research can be qualitative or quantitative. Qualitative research is descriptive and aims to explain things, while quantitative aims to quantify something. For instance, qualitative basic research can include understanding and describing the interaction between proteins, while quantitative basic research could be quantifying the strength of these interactions, or for instance, quantifying how much of a drug would have enough of an effect to disrupt these interactions. In a clinical research, another broad type of research that may be classified as applied research, qualitative would simply be looking at the relationship between two factors - i.e. exercising more increases brain activity - and quantitative would be measuring the magnitude of these effects, and using statistical tools to describe them.
To solve a problem, scientists do applied research. Drug discovery is a form of applied research as one tried to treat or cure a diseases. Most engineering researches are also applied researches as one tries to develop and improve existing technology. To answer questions and understand the fundamental principles underlying certain concepts, scientists do basic science. Identifying and understanding proteins involved in a disease is a kind of question a basic scientist answers. In general, these do fields often intersect with each other as the fundamental understanding of nature will often result to a technology that betters human life - or a problem usually warrants understanding of a basic concept.