The most direct effect a grant can have on your educational goals is that it can free you from financial limitations. Education is expensive. If you cannot afford to pursue your degree at your top school, you may have to pursue a degree at a lower-ranked school, which will limit the options of cutting-edge courses to take. Grant funding can help improve your financial situation to the point that there are no financial limits on your school choices, which will help you academically and professionally.
Grant funding is quite different from scholarship funding. Typically, scholarship funding is granted to you on the assumption that you will do something very specific with the money. For example, if you win an academic scholarship, you can only use the money on the condition that you play on a designated sports team. Once you get your grant money, on the other hand, you simply have money in the bank, and can use it in any way you want. With a grant award, there is less restriction on your academic options.
Having a grant on your resume will make you look attractive to certain schools. For example, winning a very distinguished grant from a medical charity will look good on a medical school resume. Furthermore, you are not obligated to disclose the grants you have won on your resume, so if you won a grant from an organization that is somehow controversial, you do not need to disclose the information. Grants can have a positive effect on your resume when they are awarded by prestigious, neutral organizations.
Winning a grant can have spillover effects on your academic career that are not related to the grant itself. For example, if you apply for a grant from an educational institution, the process of interviewing for that grant may introduce you to academically influential people. If you take advantage of the connections you build from your grant applications, you can use these connections to get advice and recommendations for other academic programs in the future.