In research proposals, why do investigators need to claim a certain fraction of their salaries, from the proposed budget? In research proposals, why do investigators, who usually are permanent faculty members, need to claim a certain fraction of their full-time salaries, from the proposed budget? Are they not paid in full by the university?
There are several reasons in the US. Most faculty are paid for 9 months of the year not 12. They may choose to spread out their pay into 12 payments a year, but their base salary is for 9 months. Grant funding is one way to supplement their pay up to a full 12 months. Unfortunately, the National Science Foundation, which funds a lot of academic research in the US, only allows a maximum of 2 months to come from NSF, so professors must diversify somehow as well. 

Additionally, some faculty may choose to buy out some of their required teaching. Many departments will allow you to teach less if you can bring in even more of your salary. Sometimes this is done with grant funding, but I think more often it is done using endowed chairs.