Why does the construction of 要是…的话 mean "if"?
If you find these kinds of things puzzling, I suggest you try and download 现代汉语八百词. It gives meanings and uses of a lot of these constructions. As Huang says, these constructions mean just what they mean. 

On page 594 of 现代汉语八百词 it says (the page number will depend on the edition you download):

要是 yào.shi

［连］表示假设；如果。

a) 用于前一小句。

～看见《汉英词典》，替我买一本 | ～他不去，你去吗？

b) ‘要是...’后可加‘的话’。‘要是...的话’可用在后一小句。

～有人问的话，说我在老马家 ｜ 坐船去好，～来得及的话

c) 要是 ＋ 名。

～别人（＝如果换了别人），这事不一定能办成 | 老同学聚会真不容易，～去年，咱们还聚不齐呢！



Meaning is roughly:

yào.shi

[Conjunction] expresses hypothesis; if.

a) used in first clause.

If you see a "Chinese-English Dictionary", buy one for me | If he doesn’t go, will you go?

b) 的话 can be added after 要是. '要是…的话' can be used in the second clause.

If anyone asks, tell them I’m at Ma’s place | It’s good to go by boat, if you can make it.

c) 要是 + noun.
If someone else (= if it were someone else), this matter could not necessarily be accomplished | It’s not easy for old classmates to get together, if [it were] last year, we couldn’t have done it!