This user research methodology focuses less on the user himself (role, "persona", demographics, etc.), but rather on the context (situation, circumstances) in which a concrete need (job) occurs or arises.
A user hires a product for a specific job to achieve a particular outcome (in short: to get a job done). The approach allows to uncover underserved needs, implicit motivations and indirectly also why a user prefers a product to another to do the job.
It's important and helpful to always try to find out which jobs are relevant to a user instead of just asking him which feature they prefer. (Because a feature is always only one possible solution to a problem. There might be others which solve the problem in a better way.)
The Nielsen Norman Group recommends to combine Personas and Jobs to be Done, as "the usability of any given design can only be assessed relative to two variables: who are the users and what do they need to do? That’s why it’s critical for the validity of a usability study to recruit representative test users and give them representative tasks to perform."
Job Story
Gained insights can be represented in job stories:
"When [situation], I want to [motivation], so that I [expected outcome]".
More information
Many helpful, sometimes controversial and detailed information can be found in the linked sources.
There's also a useful step-by-step description in the TiSDD method library which is an additional PDF (free download) to the book "This is Service Design Doing" (TiSDD). The steps below are a modified version of this based on own insights and experiences.
Anything to improve with the method description? Just send an e-mail with your suggestion. Thank you!