Is innovation an idea or a culture and how do you create it at work?

It is both! It comes from the creative capacity of individuals but it also thrives in an environment conducive to new ideas. You create it by building trust. No trust = no innovation.

currently, I am in charge of educational affairs unit. Basically, I am responsible for preparing schedules and assigning teachers to classes. even, I hold a weekly meeting with teachers to get knowledge about the progress in their teaching process and likely obstacles that  might occur inside the class.

Innovation as culture of an organization is more effective rather than passing it off as an idea

Any Idea That to develop the orgaizations position is an innovative idea which can be effective through impliment it as a team and each and every person take the leadership of their own responsibility..

An innovation is an idea that has been implemented.  In other words, you have to think of something and then do it. 

Thinking of something is very easy in practical terms - you just think of it.  Making it happen is much harder.   However, really good ideas are hard to think of.  This is why good innovations are rare - they require a good idea followed by good implementation.

Organisations are usually organically resistant to change, which makes innovation difficult.