1 endeavour, strain, struggle, make every effort, attempt, try (hard), do one's best or utmost, exert oneself, work at, Colloq give (it) one's all, go all out:
Jim strove to keep his self-control. Jennie strives for perfection in all she does.
2 compete, contend, fight:
One must often strive against unbelievable odds to achieve a goal.