of its own accord:自发地；自动地
of在这里的用法就是普通的“of+名词”,没有什么特殊的含义,of its own accord就是一个固定搭配,记住意思就好了.
of+名词：I read this book out of interest.我读这本书是因为我对它感兴趣.(of+interest)
...in order to interpret (with confidence) the extent to which recent changes are natural as opposed to being the result of human activities.
...来证明最近的气候改变到底有多少是自发性的,又有多少是受到人类活动影响的.
这后半句话主干是interpret the extent
to which...是extent的定语从句.to some extent:在某种程度上
as opposed to：与…相反；as opposed to being the result...与…（说法）相反
recent changes are natural as opposed to being the result of human activities.意思是：最近的改变并非人类活动的结果,而是natural的（自然发生的结果）.
但由于之前有个extent,也就是说“这种说法在哪种程度上是真的”的意思,因此我翻译为“...来证明最近的气候改变到底有多少是自发性的,又有多少是受到人类活动影响的”.