This is the 14280th most frequent Russian word.
осуществлять
To carry out, implement, or fulfill.
In this sentence, 'осуществлять' is used to mean putting into action one's aspirations or goals, emphasizing the undertaking of realization.
Я стараюсь осуществлять свои мечты и цели.
I strive to realize my dreams and goals.
Here, 'осуществлять' refers to the implementation or the active execution of supervision and control in accordance with laws.
Власти должны осуществлять контроль над соблюдением закона.
Authorities must exercise control over compliance with the law.
Though 'осуществлять' is in the past tense here, it conveys the process by which the project was brought to completion through actions.