Humans, even at a very early age, can learn visual concepts and understand geometry and layout through active interaction with the environment, and generalize their compositions to complete tasks described by natural languages in novel scenes. To mimic such capability, we propose Embodied Concept Learner (ECL) in an interactive 3D environment. Specifically, a robot agent can ground visual concepts, build semantic maps and plan actions to complete tasks by learning from human demonstrations and language instructions. ECL consists of: (i) an instruction parser that translates the natural languages into executable programs; (ii) an embodied concept learner that grounds visual concepts based on language descriptions/embeddings and a pretrained object proposal network; (iii) a map constructor that estimates depth and constructs semantic maps by leveraging the learned concepts; and (iv) a program executor with deterministic policies to execute each program. ECL has several appealing benefits thanks to its modularized design. Firstly, it enables the robotic agent to learn semantics and depth unsupervisedly acting like babies, e.g., ground concepts through active interaction and perceive depth by disparities when moving forward. Secondly, ECL is fully transparent and step-by-step interpretable in long-term planning. Thirdly, ECL could be beneficial for the embodied instruction following (EIF), outperforming previous works on the ALFRED benchmark when the semantic label is not provided. Also, the learned concept can be reused for other downstream tasks, such as reasoning of object states.