This is the 14298th most frequent Russian word.
ответственной
Responsible.
In this sentence, 'ответственной' is used as an adjective in its instrumental case form, describing Maria's given responsibility or role.
Мария назначена ответственной за проект.
Maria has been appointed as responsible for the project.
Here, 'ответственной' is in its form for an attribute describing a subject (assumed female) who needs to exhibit responsibility.
В трудные времена важно быть ответственной за свои поступки.
In difficult times, it is important to be responsible for one's actions.
In this example, 'ответственной' serves as an adjective describing the steady characteristic of being responsible attributed to a female subject.