There could be numerous reasons and a right answer is difficult. 1. The apps previously opened/installed may be starting new services when they require. 2. Though you do not open any application, many apps run on background. 3. All apps are not perfect, when an apps memory management is not proper, it uses up extra RAM even when it doesn't need. 4. Bugs in apps...
lot of reasons. When you have too many apps installed, you can see RAM being used up immediately after switching on the phone, even before you start any app, this is because of the background processes they run.
What happens? your phone becomes sluggish, apps start crashing, unexpected app behaviour. Android OS has good memory management, it continuously monitors and closes any apps that are not being used and reclaims the memory when needed.
It is also a good idea to restart the phone atleast once a day.
The widgets you place on the home screens also run background processes, messenger apps like whatsapp, viber, bbm are always running in the back. Mail apps keep checking mails, the accounts you configure in android are always synced in the background unless you specifically turn sync off. All these add up.