There is a million reasons to seek help from an agent. Situations vary, from budgetary savings to "the only HR manager has quit the job" emergencies. But let's not dwell on all the possible options, and talk about the most popular reasons to contact a recruiter.
Yes, we're serious about the budget. It's only at first glance that an agency looks like an extra line of expense. In fact, if you do the minimum math, an agency saves the company a lot of money, and here's why:
Sometimes the team does not have an in-house HR manager. This is often the case in startups and small companies, and you have to burden the team leader with the search for a new employee.
The in-house HR manager may be busy with other projects, while the company may not have an internal technical recruiter (a more specialized professional who is solely responsible for sourcing and it recruiting).
When such a recruiter does exist, they also have their own workload. It's not alright to triple their workload if you suddenly need to find three times as many candidates without delaying the search - for example, when launching a new project, when the company is growing rapidly, or when opening a new line of business.
Sometimes, agencies are approached in order to find a highly rare or best of the best specialist. Or both. Finding such a unicorn needs a lot of resources, expertise of technical recruiters, extra pair of hands to widen the funnel, alternative search sources, advanced sourcing. Recruiter's candidate database and people network are a good help too.
One more case is when you need to search in another country, so a person who will conduct interviews in a foreign language comes in handy. This is common when a company expands into a foreign market, opens an office somewhere else and becomes global.