The question asks for the literal meaning, so the word has to be broken into its parts.

Upanishad is formed from upa, meaning near, ni, meaning down, and the verbal root shad, meaning to sit. Put together they yield sitting down near — the disciple seated close to the teacher to receive instruction.

The etymology describes the actual mode of teaching. This knowledge was not delivered to a crowd but transmitted in intimate, often secret sessions to a pupil judged fit to receive it, which is why the Upanishads are also called rahasya or secret doctrine, and why the tradition is known as shruti, that which is heard.

Learning by heart all mantras describes the memorising discipline of Vedic recitation, preserved through techniques such as pada-patha and krama-patha, but that is not what the word means.

Sub-parts of the Vedas is a positional description rather than a literal meaning. The Upanishads do form the concluding portion of the Vedic corpus and are therefore called Vedanta, the end of the Veda, but that is where they stand, not what the name says.

Stories of masters and disciples is closer to the narrative content of the Puranas; the Upanishads are philosophical dialogues concerned with Brahman and Atman.

Hence `Upanishad' literally means sitting near the Guru to learn.