that在句中的意思,并解释为什么用would,是什么语法现象This time he was barking so that someone would let him

so that = 这样地...以至于....
Would =是第三人称的过去将来时。
was barking = 过去进形式；
这次他曾这样地大喊大叫，以至于有人就让他走开了。

so that 在此处引导的从句应用虚拟

so that 以至于/目的是= in order that 引导目的状语从句
would 是过去将来时态,前面有个was,是指was时候的将来,即希望他们会把他放出去