The subject of a sentence is the noun or noun phrase that the verb agrees with. In English, that is the part that the verb matches for number (singular or plural) in the simple present tense in the third person:
Jennifer prefers Oasis
Jane and Mary prefer Blur
In Spanish, the verb always agrees with the subject for number and "point of view" or person (I/we, you, he/she/they).
Omission of subject pronouns
When the subject would have been a pronoun, it is usual for the subject not to be explicitly stated at all. Instead, the subject pronoun that would have "filled the gap" is generally indicated by the verb form (which still agrees with it), or else must be deduced by the speaker (in many subjunctive forms, for example, the I and he/she/it forms are identical).
Note that this does not mean that subject pronouns are "optional". In many cases, it is actually ungrammatical to use the subject pronoun. Subject pronouns are generally only used for certain pragmatic reasons such as emphasis, contrast or focus.