What is a provisional patent application, and how is it different from a non-provisional application? (and what's the EU equivalent?)

A provisional patent application is a lower cost, 12 month placeholder that secures your filing date without formal examination. It never becomes a patent on its own. A non provisional application is the full, examined filing that can actually grant. USPTO fees for a provisional run roughly $65 to $325 depending on entity status, compared with about $1,820, $910, or $364 for a non provisional filed as standard, small, or micro entity respectively. The EU has no provisional application at all. Instead, a first filing at a national patent office or directly with the EPO starts a 12 month priority year under the Paris Convention, during which a later EP filing can claim that same priority date. In both systems, a thin or vague first filing can weaken or void the priority date it was meant to protect.

Sources: USPTO, Provisional Application for Patent, WIPO, Paris Convention.