What is actually robotics?
Probably quite many people, particularly common people (i.e. people not working in the field), have partial or incomplete understanding about robotics. Of course robotics is related to robots, a word coined in 1920 with meanings associated with labor and was firstly used to denote a fictional humanoid. Although a robot can refer to either a physical robot or a virtual software agent, the latter is more commonly called a bot. The term robotics, however, has nothing to do with bots. Robotics only deals with physical robots (or simulated physical robots). In a short expression, robotics is a study about robots or a know-how about robots.
Quite many people probably think that robotics is only about programming a robot. This is not completely wrong, but it is a very partial and incomplete understanding about robotics. In fact, robotics is an interdisciplinary field of study. Referring to the traditional taxonomy of engineering, robotics can be seen as an intersection between mechanical engineering, electrical & electronics engineering, and computer & software engineering. As control engineering and artificial intelligence (AI) emerged as new disciplines/fields at a later stage in the history of science and engineering, robotics can also be seen as an intersection of five fields of study: mechanical engineering, control engineering, electrical & electronics engineering, computer & software engineering, and AI. This is shown in the following diagram:

Although control engineering is quite common to be mentioned as a branch of engineering, control is typically studied in mechanical engineering and electrical & electronics engineering. Control is a common subject in both the engineering branches. AI in its history emerged from the computer & software engineering. Hence, the three compositions and the five compositions of robotics as earlier described are basically not contradictory. It’s just two ways to say almost the same thing.
What is a robot?
To understand robotics better, it is good to know what actually a robot is. Some people define a robot as “a machine that moves”. Of course the movement or motion here is more general than locomotion (i.e. motion that makes a robot mobile), as not all robots are mobile. In fact, most of industrial robots make their motions while they are stationary, meaning they have arms that move with stationary bases. Later some people define a robot as “a machine that moves and has intelligence.” The question arising would be: “What is intelligence?” The control, typically closed-loop control based on feedback, is also a type of intelligence as a control system basically acts based on a certain knowledge, algorithms, or mathematics after it senses some physical conditions/parameters. The definition of control itself grows from not only low-level control but also high-level control. Of course nowadays people are heavily discussing AI as a sort of intelligence that can be embedded to a robot. Actually, when applied to a robot, AI usually becomes a part of the high-level control of the robot.
Basically, every robot has two main elements: body and brain. One may also say that a robot has three elements: body, nerves, and brain. Both are fine, as nerves basically connect the body to the brain. The nerves can also be seen as part of either body or brain. It doesn’t matter.
Traditionally, the body of a robot is the physical structure and mechanism that composes a robot while the brain of the robot is the control system applied/embedded to the robot. The sensors and control & communication cables can be seen as the nerves of the robot. It is impossible to have a robot with only body (as it would be only called a mechanism) or a robot with only brain (as it would be only called a software).
What should I learn to major or work in robotics?
As robotics is an interdisciplinary field, people majoring and having a career in robotics may come from various backgrounds. Some come from mechanical engineering, some others come from electrical & electronics engineering, some others come from computer science or software engineering, and so on and so forth. This is very common due to the interdisciplinary nature of robotics.
With various possible backgrounds, one dealing with robots however should study a lot of things related to different aspects of a robot. While this can be achieved by a collaboration of people from various backgrounds in a team, one should try its best to understand the different aspects of robotics. Such multidisciplinary mastery would be a great advantage for someone working in robotics.