The path can either be full or relative (of course if the image is from another domain it must be full).
You don’t need to use quotes in the URI; the syntax can either be:
background-image: url(image.jpg);
Or
background-image: url("image.jpg");
However, from W3:
Some characters appearing in an unquoted URI, such as parentheses, white space characters, single quotes (‘) and double quotes (“), must be escaped with a backslash so that the resulting URI value is a URI token: ‘\(‘, ‘\)’.
So in instances such as these it is either necessary to use quotes or double quotes, or escape the characters.