The term subject has different meanings in different sciences.
For example, the term stands for an unique entity in philosophy. This entity owns unique consciousness and unique experiences.
In linguistics, a subject is a part of a sentence. This part is formal (different length –one or more words) and functional (takes a grammatical task) determinable. In some languages like Latin or German, the subject stands in nominative case. It is the answer to the questions ‘who’ and ‘what’ in the clause. Thereby it says about whom the sentence is made. The subject agrees with the verb in numerus and genus (only with a finite active verb; in passive constructions the subject does not have to agree).
The subject usually takes the semantic role of an agent (actor).
The subject is one of the two main constituents of a sentence, the other one is the predicate.