Breakdown of Şemsiyem var çünkü yağmur yağacağını biliyorum.
var
there is / existent
bilmek
to know
yağmur
rain
yağmak
to rain / to snow
Questions & Answers about Şemsiyem var çünkü yağmur yağacağını biliyorum.
How exactly is the word yağacağını built?
It comes from the verb yağmak (to rain). To say "that it will rain", we add the future participle -acak (which softens to -acağ), followed by the 3rd person possessive suffix -ı, the buffer letter -n-, and finally the accusative case suffix -ı.
Why does yağacağını need the accusative case at the end?
The whole phrase "that it will rain" acts as the direct object of the verb biliyorum (I know). Because you are stating the specific thing you know, the complement clause requires the accusative case marker -ı.
The subject of these clauses usually takes the genitive case. Why isn't it yağmurun?
You are right that the subject of a complement clause normally takes the genitive case (for example, Ali'nin geleceğini meaning "that Ali will come"). However, yağmur yağmak is a tight set phrase. When the subject is a general, non-specific concept like rain, the genitive suffix is often dropped. Saying yağmurun yağacağını is also grammatically correct, but leaving it as yağmur is very common and natural.
A quick reminder: why do we say şemsiyem var instead of using a verb for "have"?