这里的 hat in hand 就是语法上所谓的独立主格结构。字面意思是“手里拿着帽子”，但通常引申指“恭敬地”“毕恭毕敬地”“诚恳地”“低三下四地”等。如：

He stood there, hat in hand. 他站在那里，手里拿着帽子。（在特定语境中也可理解为：他恭恭敬敬地站在那里。）

He asked for help, hat in hand. 他毕恭毕敬地请求帮忙。

He came to me, hat in hand, asking if I could get him a job at the company. 他毕恭毕敬地走到我面前，问我能否在公司给他安排个事做。

有时也说 cap in hand。如：

Elderly people should receive a heating allowance every winter, instead of having to go cap in hand to the government. 老年人应该每年冬天都能领到取暖费，而不是向政府低三下四地讨要。

网友句子：I come to you, hat in hand, to apologize for the damage I had indirectly caused and to ask you to reconsider my lifetime ban from the hotel. 我来找您，诚恳地为我间接造成的损害道歉，并请求你重新考虑禁止我终身入住酒店的问题。

补充：“名词+介词+名词”类独立主格结构的更多例句：

A girl came in, book in hand. 一个女孩进来了，手里拿着书。

He sat back, glass in hand. 他手里拿着酒杯向后一靠。

He dashed into the room, gun in hand. 他端着枪冲进屋里。

She sat, pen in hand, searching for the right words. 她手拿钢笔坐在那里，在脑海中搜寻合适的词。

Sylvia, camera in hand, asked, “Where do we go first?” 西尔维娅手里拿着相机问道：“我们先去哪里？”

He stood there, pipe in mouth. 他站在那里，嘴里叼着烟斗。