First, let's assume that you're applying for a position, where your research matters. If so, then the hiring committee wants to judge as best as it can whether you will do good research after you're hired. Also, let's assume that the hiring committee is not familiar with your specific area of research, so it is not able to judge directly the quality of your work by reading it.
Published and accepted papers, as well as grants awarded, are very useful for establishing the strength of your research ability. Other measures such as quality of journals and citation numbers can strengthen your case even further and are in fact quite important if you are applying to a strong department.
Submitted papers, preprints, and grant applications do not help in judging your research ability. But they do matter. In particular, they, along with the items above, show that you are committed not only to continuing your research but also documenting it in a way that your department, your university, and your peers can judge it properly. In short, it provides evidence that you're willing to and are continuing to "play the game". This stuff won't help you beat out someone who is viewed as a stronger mathematician than you, but it might help you beat out someone viewed as on the same level but does not demonstrate the same level of explicit effort.
You should provide all evidence of research activity, whether it represents something you've already accomplished or something you are still striving for.
And you should omit anything that a hiring committee might choose to interpret as a serious distraction to your research efforts.