To seek is to look for something. This word is not especially common in regular, everyday English ("Look for" is much more common.), but it’s one of those words you should know because you hear it occasionally. The word "seek" is more commonly found in written English.
They’re seeking the advice of a doctor.
The young man traveled to India to seek the wisdom of a guru.
Linda is seeking a new job in the travel industry.
A couple of raccoons sought shelter inside a hollow tree. (The past tense of "seek" is "sought.)
The refugees sought protection from United Nations troops.
Prosecutors sought a 15-year sentence for the woman accused of drug trafficking.
The raccoon seeks shelter.
The past participle form of "seek" is sometimes used as an adjective when combined with the preposition "after."
This much sought-after piece of furniture is very valuable.
Dan has work skills and experience once sought after by several companies, but now he can’t find a job.
Long-sought solutions to the conflicts in the middle east are still out of reach.