POCO stands for "Plain Old C# Object" or "Plain Old CLR Object", depending on who you ask. If a framework or API states that it operates on POCO's, it means it allows you to define your object model idiomatically without having to make your objects inherit from specific base classes. Generally speaking, frameworks that work on POCO's allow you greater freedom and control over the design and implementation of your classes, because they have fewer requirements to work correctly.
Persistence ignorance means that, as much as possible, anything in your code operating at the business logic layer or higher knows nothing about the actual design of the database, what database engine you're running, or how or when objects get retrieved from or persisted to the database. In the case of the MEF, persistence ignorance is attained by working on POCO's and using LINQ to perform queries (i.e., not requiring the user to create any SQL queries to retrieve the desired objects).
It's an open question, but it's generally agreed that under most circumstances, the domain objects (or business objects - either way, the POCO's mentioned above) should be ignorant of persistence logic. Meaning, instead of calling MyBusinessObject.Save(), you have a IO manager or adapter class, and you call Manager.Save(MyBusinessObject). In this way, you avoid exposing persistence semantics on your business objects - you get better separation of concerns that way.
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