What is the difference between a broadsheet and a tabloid newspaper?

These terms refer to the size of the newspaper page. The distinction is blurring as newspapers shrink their page size. 

However, probably the easiest distinction is the way the paper reads and the position of the fold.

On a broadsheet, the paper is folded in half and the type is printed from above the fold to below the fold (top to bottom.)  On a tabloid newspaper, the paper is still folded in half, but the type runs from left to right (for languages that read left to right.)

In a tabloid newspaper, there is a "gutter" of white space in the fold where type cannot be printed because the ink would smudge.

In the exact center of a tabloid it is possible to run text completely across the page, but this is rarely done except for advertising.

There is a third size of newspaper called the "Berliner" which falls somewhere between the two sizes. The text on a Berliner runs from above the fold to below.