Without getting too technical, a C corporation is what most large corporations are registered as. They pay corporate tax on earnings and have periodic reporting requirements to the local corporation commissions. You need to hold shareholder meetings and there are several other requirements.
An LLC gives you the same limited liability of a C corporation but doesn't require the corporate taxation or periodic reporting or shareholder meetings. Many small businesses are registered as LLCs to protect the owners personal assets. You can elect to be treated as an S corporation for tax purposes, which means that the LLC will need to operate as a pass-through entity and pass on earnings and losses directly to the owners.