An electric circuit is a loop around which an electric current flows. Every real circuit has resistance and impedance, and some source of electrical energy which may be called a generator.
Electric circuit analysis is the business of figuring out how electric energy flows in a given circuit. It always seems to involve a bit of hand waving*, yet somehow seems to come up with more less the right answers. Most of the time.
* I am not saying that the whole science of electromagnetism is rubbish (as Old Miner seemed to think). However, in applied engineering, there is often a massive difference between the theoretical analysis and the circuit you solder together. In fact, much work is done using "rules of thumb" and other simplifications. Even then, unexpected "real world" (can unreal ones exist?) factors often cause differences between the mathematical model and reality. That's what makes it fun ... sometimes !