The main advantage of forming an LLC vs. a sole proprietorship or partnership is the greatly diminished risk to your personal finances. By forming an LLC, you shift responsibility for your business debts and liabilities from yourself to the newly formed corporate entity (thus, "Limited Liability Company"). So, generally speaking, if someone successfully sues your business or your business goes into a substantial amount of debt, creditors can only touch the assets you've put into the business.
So, for example, you would set up a separate checking account for your LLC, and if your business ends up owing a bunch of money, anything in that account is fair game, but your personal checking account would be off-limits, as would be your home and personal vehicle.
The primary disadvantage of forming an LLC is that you'll have to do a fairly substantial amount of paperwork and pay some fees to start and maintain the LLC. In Florida, it's $125 minimum to file, plus $138.75 each year with your annual report.
Long story short, if you're doing contract or gig work and business is good, there will eventually come a time where it makes sense to form an LLC. Whether that time is now for you depends on whether the hassle, administrative work and fees are worth the reduced risk given the current size, profitability, and future growth potential of your business.
(DISCLAIMER: I am neither a lawyer, accountant, nor financial advisor, and this information should not be taken as advice in lieu of consulting with a certified financial planner and tax, legal, or other professionals.)
LLC Asset Protection In-depth Overview