The Entity Framework opens connections only when required, for example to execute a query or to call SaveChanges, and then closes the connection when the operation is complete.
From Martin Fowler’s book Patterns of Enterprise Application Architecture in respect to Unit Of Work.
When you're pulling data in and out of
a database, it's important to keep
track of what you've changed;
otherwise, that data won't be written
back into the database. Similarly you
have to insert new objects you create
and remove any objects you delete.
You can change the database with each
change to your object model, but this
can lead to lots of very small
database calls, which ends up being
very slow. Furthermore it requires you
to have a transaction open for the
whole interaction, which is
impractical if you have a business
transaction that spans multiple
requests. The situation is even worse
if you need to keep track of the
objects you've read so you can avoid
inconsistent reads.
A Unit of Work keeps track of
everything you do during a business
transaction that can affect the
database. When you're done, it figures
out everything that needs to be done
to alter the database as a result of
your work.
Whenever I use Entity Framework for a clients (which I'd admit is rare) the ObjectContext object is the Unit Of Work implementation for the system. That is the ObjectContext will somewhat meet the three statements above. Rather than concentrating too much on the absolutely correct definition using the ObjectContext makes things a little easier for you.
Do some research on DI/IoC and Repository patterns this will give you more flexibility in handling your problem.