A "recruiting agency" is a company that finds employees for other companies. If you need to find a certain kind of employee, but it takes too long to find people like that, you can hire a recruiter to find the right person for the job. Recruiters will often call people who are already working at other companies, and will try to convince those people to change their jobs.
There's also another word for recruiting agents. People call them "headhunters". "Headhunter" is also a word to describe members of native tribes in places like South America who kill their enemies and take their heads. So, as you might expect, the word "headhunter" is not a very positive way to refer to a recruiter!