This is the 945th most frequent Turkish word.
koca
Husband; big/large.
Here, 'koca' refers to the speaker's husband, a marital partner. It is used as a noun in its possessive form.
Çok sevimli bir kocam var.
I have a very lovely husband.
In this context, 'koca' means 'huge' or 'gigantic,' and it is used as an adjective to describe the mountains.
Şu koca dağları aşmamız gerekiyor.
We need to cross those huge mountains.
Here, 'koca' as an adjective emphasizes the scale of the mistake, meaning 'big' or 'grand' metaphorically rather than literally.