1.the rat that ate the meat：that引导定语从句,吃了肉的那只老鼠,去掉that就成了the rat ate the meat,cat是主句的主语,所以显然不对.
2.the meat that lay in the house.同上
3.the house Jack built.杰克建的屋子.
不知道你有没有发现前两句that后面是动词,其实第三句也可以改成the house that built by jack.
that是关系代词,用于从句中缺少成分,常在从句中充当主语、宾语或表语
e.g:This is the park that I usually go to.--to后面缺少了宾语,用that充当
This is the park that has a big lake.--从句缺少主语,用that充当