It turned out that the company that had been hired to organize it did not keep their word.

keep 的意思是"保持、遵守"，在这里指"遵守诺言"。 their 是代词 they 的所有格形式，指代前面提到的"公司"。 word 在这里不是指"单词"，而是指"诺言、承诺"。 keep their word 是一个固定短语，意思是"遵守他们的诺言"或"履行承诺"。