put是放的意思，foot是脚的意思，put one's best foot forward是全力以赴的意思。

【例句】
Each one had to put his best foot forward because they weren't given another chance to show off their talent.
每个人都必须全力以赴，因为他们再也没有机会展示自己的天赋了。

Put one's best foot forward Tina dresses smart in the news conference and hopes to put her best foot forward.
蒂娜在记者会上盛装打扮，希望能给人留下好印象。