The term "S corporation" means or refers to a

small business corporation for which an election under section 1362(a) is in effect for any said year. 

Translation, for a single owner, its basically the same as a partnership without the partner.
For multiple owners, it constitutes an entity whereby by each owner has a stated interest. Individuals and charitable organizations may be shareholders.

An S-Corp files taxes in the same manner as a partnership where each shareholder pays taxes only on their portion of the profits. Personal deductions and credits will be considered when calculating the income tax on profits. Profits are typically exempt from self-employment tax.

An S-Corp is a federal only election that must be applied for within a certain time frame in order to be effective for any given year. LLCs and

Corporations may elect to be taxed

as an S-Corp.