There are two basic kinds of Fulbright grants available to students: English Teaching Assistantships and academic grants for research or study. Each requires a very different kind of recommendation but both types seek to determine both personal and academic suitability for the grant being sought.
The ETA recommendation must respond to specific prompts. Characteristics such as strong communication skills, demonstrated interest in teaching, tutoring or mentoring, maturity, adaptability, and genuine interest in engaging with the host culture are all desired. See the specific questions asked of ETA recommenders here.
Recommendations for academic grant applicants should ideally address the quality and preparation of the applicant as well as the feasibility and value of the project being proposed. The applicant should provide you with at minimum an abstract if not a draft of the proposal if you haven't already been involved in its formulation. It can be very useful to comment on why the project proposed must be done abroad if it is not obvious and also the role it might play in the applicant's future. See the specific information asked of academic grant recommenders here.