A volitional/exhortative form of 頑張る used to encourage oneself or others: “let's do our best” / “let's go for it.”
試験まであと一週間、みんなで頑張ろう。
One week left until the exam — let's all do our best.
最後の1キロだ、もうひと踏ん張りして頑張ろう。
It's the last kilometer — one more push, let's go for it.
朝、鏡の前で『今日も頑張ろう』と自分に言った。
In front of the mirror this morning I told myself, 'Let's do our best today too.'