JR pass can be used on JR lines only. Many big cities have JR lines, but most (if not all) also have private railways - the JR pass cannot be used on those lines.
Most long-distance inter-city lines are JR (including the Shinkansen=bullet trains), and are what you will need to get around Japan.
The JR Pass is useful in the city, but is more meant to be used for getting across the country, and you should try to optimize your usage of the JR pass so you always are able to use it when traveling long distances. Inside the city, you will often use cash when private lines are more convenient.
"Subway" merely means a subterranean trainline. There are JR subways, non-JR subways just as there are JR lines and non JR lines.