How important is outreach for applying to tenure track professor position?

Pertinent to academia, I think of outreach as activities that bring academic subject matter and/or expertise to a community audience, often an audience that is under-served. Activities might include lectures or presentations to community audiences presented in laymen’s terms about subjects that are esoteric but interesting; interacting with elementary students to make a topic (like programming) more understandable or to engage them in the scientific process; mentoring high school students doing a science fair project. There are others.

The degree to which describing involvement in outreach might help an application for a tenure-track position may depend on factors specific to the institution and its values; the teaching responsibilities of the assistant professor position; and the degree of prior involvement in outreach. For example, a university that has a stated commitment to the community in which it resides might place high value on prior involvement in outreach because outreach aligns with the values of the institution. If the specific department has an outreach program (e.g., it holds regular coding camps or has a formal affiliation with an elementary school) prior involvement in outreach might strengthen the application because it demonstrates experience relevant to the department. Outreach that has involved interactions with students at any level may be more important when the Assistant Professor position will involve teaching undergraduates because it provides some evidence of prior experience in teaching/interacting (hopefully) positively with young people. But the outreach should be clearly and unambiguously meaningful. “I spent 1 week as a counselor at a math camp” probably doesn’t help and may hurt.

Finally, in a space-constrained CV, description of outreach should not displace documentation of specific requirements of the position (e.g., education, research experience, involvement in professional societies, publications/presentations.)

The goal of the CV should be to “market” yourself for the position. If you’ve documented what needs to be documented and documenting outreach might help your application, include it.

At most universities, outreach is not part of the formal hiring criteria. Even when it is part of the criteria, it is not one of the important criteria.

However, you might be asked during a job interview, "How do you engage with the community?" or "How will you participate in recruiting students?" You should have outreach experience you can use as an example to answer that question.

Scientists should do outreach because it benefits the public. Do not expect a reward.

most universities limit the page numbers of a CV submitted during the application process

This is not true for tenure track positions.