"As railways developed and expanded one of the key issues to be decided was that of the rail gauge."

what do "that" and "of" mean here, i cannot fully understand. if i built this sentence, i would ignore the "that of" part, or at least "of" part. is there any difference in the meaning with and without that parts?

I am not a native English speaker but my understanding by “that of ” is its pronoun function.

"That of" is mostly used to compare two things (that is used as a pronoun).

The population of Istanbul is greater than the population of Ankara . = The population of Istanbul is greater than that of Ankara.

Likewise, in your sentence it is used as kind of pronoun which is subject of the compound sentence [one of the key issues]   in order to avoid repating it.

one of the key issues to be decided was that of the rail gauge." = One of the key issues to be decided was the issue of the rail gauge.

I´m not an English grammar teacher, but it is my native language. I will try to help.

"As railways developed and expanded one of the key issues to be decided was that of the rail gauge."

(Time part, subject verb 

Yes, in my opinion, the sentence would still have the same meaning if you didn´t use ´that of´.

"As railways developed and expanded one of the key issues to be decided was the rail gauge." (OK)

"As railways developed and expanded one of the key issues to be decided was (that of) which rail gauge to use." (more detail, and ´that of´ is optional)

"As railways developed and expanded one of the key issues to be decided was that the rail gauge." (Without ´of´ it does not make sense in English)

In America different private railway companies built railways with different gauges (rail widths).

In Australia different states built railways with different rail guages before Australia became one nation in 1901.