Hello Sam
As per my understading IRB interface is mostly required in bridged networks.
A bridge domain is a collection of tagged and untagged ports.So to route traffic out of the bridge domain and communicate between bridge domains you need the IRB interface.Check the example below
|nternet Cloud
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DSLAM(Multiple Vlans)<---->MX Router(IRB)------->BRAS
This exmple is classic scenario where the IRB can be utilized.The traffic between the DSLAM and BRAS is bridged
and to route this traffic towards the internet you need IRB .
To further understand the bridge you better read about the classic fallback bridging scenario.
You may also like to check the BVI interface as reffered to by Cisco and is equivalent to IRB interface.
A good explanation for BVI is as follows
http://serverfault.com/questions/254347/what-is-a-cisco-bvi-interface-what-is-it-used-for
Note:This all is as per my understanding.If you and some one else finds something else then please do correct it.
Thanks & Regards
Malik