This is an idiom that means "was very sick with" (See: [[rc://en/ta/man/translate/figs-idiom]])
# a high fever
"her skin was very hot"
# pleaded with him on her behalf
This means they asked Jesus to heal her from the fever. This can be stated clearly. AT: "asked Jesus to heal her from the fever" or "asked Jesus to cure her fever" (See: [[rc://en/ta/man/translate/figs-explicit]])
# So he stood
The word "So" makes it clear that he did this because the people pleaded with him on behalf of Simon's mother-in-law.
# stood over her
"went to her and leaned over her"
# rebuked the fever
"spoke sternly to the fever" or "commanded the fever to leave her." It may be helpful to state clearly what he told the fever to do. AT: "commanded that her skin should become cool" or "commanded the sickness to leave her" (See: [[rc://en/ta/man/translate/figs-explicit]])
# started serving them
Here this means she began to prepare food for Jesus and the other people in the house.