From a practical standpoint, Hyper-V Integration Components (IC) are basically drivers that connect Hyper-V to virtualized system devices. The IC must be the correct version for the host OS and VM, so version mismatches can cause some hardware devices to become unavailable for the VM.
This can happen, for example, when a later VM hosted under Windows Server 2012 is migrated to an older server running Windows Server 2003. The Hyper-V Integration Components may not be able to update, and other symptoms may occur including loss of network or I/O devices -- or there may also be a dramatic hit to the VM's performance. This can cause untold suffering in data centers where VMs must move between different OS versions.
One frequently-overlooked way to help ensure peak performance of a Hyper-V system is to install the latest IC version for every VM. Fortunately, tools like System Center Virtual Machine Manager can identify outdated Hyper-V Integration Components versions within individual VMs – this can greatly streamline the effort needed to identify update candidates.