I’m not sure how to explain the structure as a whole, so I’ll try to break it down in two parts:
The first being the sentence without parentheses:
っていますは「と言います」と同じ意味です。
“っています” has the same meaning as 「と言います」.
Literally: As for “っています”, 「と言います」is with the same meaning.
Kind of. It’s hard for me to explain grammatically because I don’t really know many of the technical terms.
Then for the parentheses:
漢字で書くのを忘れていました。
What’s going on here is the “nominalization” of a verb phrase, which is the term I’ve seen thrown around.
漢字で書く (to write in kanji) のを (the の makes it function grammatically as a noun so you can modify it, を makes it the object of an action) 忘れました (I forgot).
So, all together it means:
“っていいます” (I forgot to write it in kanji) has the same meaning as “と言います”.
As a side note, the 「って」 is just a coloquial way of saying 「と」.
I hope I did at least a decent job of explaining. :/