There are a couple of key differences between block-level elements and inline elements:
Content model
Generally, block-level elements may contain inline elements and (sometimes) other block-level elements. Inherent in this structural distinction is the idea that block elements create "larger" structures than inline elements.
Default formatting
By default, block-level elements begin on new lines, but inline elements can start anywhere in a line.
The distinction of block-level vs. inline elements was used in HTML specifications up to 4.01. In HTML5, this binary distinction is replaced with a more complex set of content categories. While the "inline" category roughly corresponds to the category of phrasing content, the "block-level" category doesn't directly correspond to any HTML5 content category, but "block-level" and "inline" elements combined together correspond to the flow content in HTML5. There are also additional categories, e.g. interactive content.
The following is a complete list of all HTML "block-level" elements (although "block-level" is not technically defined for elements that are new in HTML5).
Contact information.
Article content.
Aside content.
Long ("block") quotation.