Character count is important since many social media sites like Twitter and Facebook limit the amount of characters you can use on an update or post. Likewise, articles, essays and almost every writing you are asked to hand in are limited to a certain page or character count as well. Usually, the character count does not include white space but only counts the single characters.
If you check a document, however, you can get metadata information about the Character Count With Spaces as well. This is important since for status updates on social media, the white space between words and characters is counted for the overall character count as well.