LLC is, as far as I know, just a US thing, so I'm assuming that you are in the USA. Update for clarification: other countries do have similar concepts, but I'm not aware of any country that uses the term LLC, nor any other country that uses the single-member LLC that is disregarded for income tax purposes that I'm referring to here (and that I assume the recruiter also was talking about).
Further, LLCs vary by state. I only have experience with California, so some things may not apply the same way elsewhere. Also, if you are located in one state but the client is elsewhere, things can get more complex.
First, let's get one thing out of the way: do you want to be a contractor, or an employee? Both have advantage, and especially in the higher-income areas, contractor can be more beneficial for you. Make sure that if you are a contractor, your rate must be considerably higher than as employee, to make up for the benefits you give up, as well as the FICA taxes and your expense of maintaining an LLC (in California, it costs at least $800/year, plus legal advice, accounting, and various other fees etc.).
On the other hand, oftentimes, the benefits as an employee aren't actually worth all that much when you are in high income brackets. Do pay attention to health insurance - that may be a valuable benefit, or it may have such high deductibles that you would be better off getting your own or paying the penalty for going uninsured.
Instead of a 401(k), you can set up an IRA (update or various other options), and you can also replace all the other benefits.
If you decide that being an employee is the way to go, stop here.
If you decide that being a contractor is a better deal for you, then it is indeed a good idea to set up an LLC. You actually have three fundamental options: work as an individual (the legal term is "sole proprietorship"), form a single-member LLC disregarded for income tax purposes, or various other forms of incorporation.
Of these, I would argue that the single-member LLC combines the best of both worlds: taxation is almost the same as for sole proprietorship, the paperwork is minimal (a lot less than any other form of incorporation), but it provides many of the main benefits of incorporating.
There are several advantages. First, as others have already pointed out, the IRS and Department of Labor scrutinize contractor relationships carefully, because of companies that abused this status on a massive scale (Uber and now-defunct Homejoy, for instance, but also FedEx and other old-economy companies). One of the 20 criteria they use is whether you are incorporated or not. Basically, it adds to your legal credibility as a contractor.
Another benefit is legal protection. If your client (or somebody else) sues "you", they can usually only sue the legal entity they are doing business with. Which is the LLC. Your personal assets are safe from judgments. That's why Donald Trump is still a billionaire despite his famous four bankruptcies (which I believe were corporate, not personal, bankrupcies). Update for clarification Some people argue that you are still liable for your personal actions. You should consult with a lawyer about the details, but most business liabilities don't arise from such acts. Another commenter suggested an E&O policy - a very good idea, but not a substitute for an LLC.
An LLC does require some minimal paperwork - you need to set up a separate bank account, and you will need a professional accounting system (not an Excel spreadsheet). But if you are a single member LLC, the paperwork is really not a huge deal - you don't need to file a separate federal tax return. Your income will be treated as if it was personal income (the technical term is that the LLC is disregarded for IRS tax purposes). California still does require a separate tax return, but that's only two pages or so, and unless you make a large amount, the tax is always $800. That small amount of paperwork is probably why your recruiter recommended the LLC, rather than other forms of incorporation.
So if you want to be a contractor, then it sounds like your recruiter gave you good advice. If you want to be an employee, don't do it.
A couple more points, not directly related to the question, but hopefully generally helpful:
If you are a contractor (whether as sole proprietor or through an LLC), in most cities you need a business license. Not only that, but you may even need a separate business license in every city you do business (for instance, in the city where your client is located, even if you don't live there). Business licenses can range from "not needed" to a few dollars to a few hundred dollars. In some cities, the business license fee may also depend on your income.
And finally, one interesting drawback of a disregarded LLC vs. sole proprietorship as a contractor has to do with the W-9 form and your Social Security Number. Generally, when you work for somebody and receive more than $600/year, they need to ask you for your Social Security Number, using form W-9. That is always a bit of a concern because of identity theft.
The IRS also recognizes a second number, the EIN (Employer Identification Number). This is basically like an SSN for corporations. You can also apply for one if you are a sole proprietor. This is a HUGE benefit because you can use the EIN in place of your SSN on the W-9. Instant identity theft protection.
HOWEVER, if you have a disregarded LLC, the IRS says that you MUST use your SSN; you cannot use your EIN! Update: The source for that information is the W-9 instructions; it specifically only excludes LLCs.