Event is defined as a change of state. E.g. Port was up, now – it's down / server was alive, now it's not / door were closed, now they are open / etc. Change of state refers to configuration item (CI) or service and it helps to (proactively) maintain services and related CIs. I'm sure you got some kind of alert on your screen -> that's event. Event management process manages events throughout their lifecycle (from when they are raised until they are resolved).
Incident is unplanned interruption (or reduction in quality) of an IT service. Incident management is a process which handles (record, diagnose, resolve) incidents throughout their lifecycle.
Problem is cause of one or more incidents, where root cause of the problem is (usually) not known when problem is raised. Problem management is responsible to find root cause of (one or more) incident.
By infrastructure operation center, I assume you mean IT Operations (at least, according to ITIL). They perform daily activities (contrary to Service Desk who is actively involved in incident resolution).