He is the person for the job.
What's the meaning of "the" in the sentence?
"The" is a determiner, if a noun is determined, we can identify the noun from the context.
We understand from this that the phrase "for the job" is enough to determine the person. Therefore you understand that there is nobody else who is suitable for the job. Contrast this with the unidiomatic "He is a person for the job" which would suggest that while he is suitable there are other people equally suitable, or even more suitable.
The expression "He is the person for the job" is likely to be hyperbolic. The speaker is emphasising that the person is very well suited to the job by hyperbolically stating that he is the only person who could fit the role.
The person here means the one
the ultimate being
Wiktionary has a similar definition:
(colloquial) A particularly special or compatible person or thing.
It means he is the ideal, the best or the most suitable person for the job.
We should not attempt to analyse the words the and one individually.