Limited Liability Companies (LLCs) and S-Corps are business entities which are treated by the IRS as partnerships for tax purposes. They differ with respect to their corporate formalities, but both entities have their income taxed as "passing through" to their owners. What this means is that there is no C-Corp double taxation issue -- where C-Corp income is taxed once at the corporate level and then taxed again when it is distributed to its shareholders. LLC and S-Corp income is taxed only once as income of their respective owners.
LLCs and S-Corps are most useful for small business owners or sole proprietors who want to receive the limited liability of corporate structure but who are small enough to be able avoid dealing with the double taxation of the traditional C-Corp (among the requirements for S-Corp election is that the entity has no more than 100 shareholders). Aside from certain tax considerations, LLC and S-Corp treatment is virtually identical on the Federal and at most state levels.
The New York Problem
The S-Corp Option