Steve Jones has (yet another) great post called "Le Tour SOA - why support services are critical, but not important".
You should go read the article - but in a nutshell, Steve explains that important services are the ones that bring business values and critical services are the supporting ones that help keep the light on for the important services to function properly. 

While the post has SOA in the title. I think it is more general and is also applicable to applications or any other IT generated components. In fact it can also be applicable to IT itself as Nicholas Carr noted in 2003 when he published his paper "IT doesn't matter". Nicholas argues that IT will become akin to electricity and as such be critical for the business to continue operating but not important. As a side note I'd say I think this is might be true for traditional businesses but not for businesses where the IT is the business (such as banks, insurance companies, etc.)

Back to critical vs. important - I think this is an important for architects to make this distinction to be able to prioritize work and not confuse business value with semblance of business value due to criticality for operations. This doesn't mean you can neglect critical tasks (after all they are critical...). It is the important stuff that will bring your business the competitive edge.