My 2 1/2 year old daughter (who is speech delayed) makes a loud "humming" noise when she is eating or drawing with crayons. Why does she do this?

Self-Stimulating. She utiloizes this to help herself focus on the activity. Discuss this with your pediatrician in context with her other normal behaviors to be sure everything else is ok.
If your daughter has. receptive/expressive language delays; i.e., delayed comprehension of language &/or impaired ability to express her thoughts verbally plus verbal self-stimulation, call your state's Early Intervention Program for evaluation of her overall development as well as autism-specific testing. A more comprehensive evaluation is needed for accurate diagnosis, which guides treatment for optimal outcomes.