TL;DR
This is a gateway question. It is likely that the question is designed to filter out candidates who haven't worked on code where "failure is not an option," and to generate follow-on questions about past projects, code quality, performance under pressure, and development/testing methodologies.
Don't Guess; Ask Questions
Why do interviewers ask if one has experience developing mission critical apps?
The best way to find out what the question is really leading up to is to ask the interviewer to define the terms as they apply to the job. What does "mission critical" mean to the company? What about your experience on such projects would be useful for the company to learn during the interview?
This kind of gateway question is a great opportunity for you to learn more about the company and the job while answering the interviewer's questions. Don't squander that opportunity!
Guessing what the interviewer wants never works out well for either the job-seeker or the employer. Think of this as a test of your active-listening skills, and ask discerning questions when appropriate.
The General Case: Your Value Proposition
"Mission critical" has a definition. Wikipedia says:
Mission critical refers to any factor of a system (equipment, process, procedure, software, etc.) whose failure will result in the failure of business operations. That is, it is critical to the organization's 'mission'.
However, many businesses also use the phrase to mean:
- A highly-visible project.
- A politically-charged project.
- A project management death march.
- An under-funded, under-staffed project that is doomed to failure from the start, but all blame will be placed on the hapless team members.
Whatever people mean by it in a specific context, the point is that the "powers that be" generally care about the outcome or perceived value of their projects. By asking you about your experience on such projects, you're really being asked:
- if what you did mattered to anyone in authority, and
- whether your skills were sufficient to effectively deliver on important tasks.
Think about it this way: if your past employers made money building cars, but the most important thing you were ever responsible for was unit-testing the cup-holder, would you be considered a potential asset to the interviewer? Alternatively, if you were responsible for programming the chips that control the engine, but your code was so buggy that 10 billion auto parts had to be recalled, should you be considered for a job that is essential to the company's core revenue stream?
Be prepared to talk about the value of your work in the context of your past employment. Just make sure you ask enough questions to know what the interviewer might find valuable!