+1 for using Tobira, that's chapter 1 I'm sure. :)
There is nothing special about と呼ばれる. Basically that's simply the particle と plus the verb 呼ぶ that, conjugated in the passive form, becomes 呼ばれる.
The verb 呼ぶ has several meanings and usages, the most common being "to call out (to) / to call / to invoke / to summon (a doctor, etc) / to invite.. and some others. Therefore, in the passive form we can translate it as "to be called".
The particle と is used simply because the verb 呼ぶ, when used to indicate how something is named, requires the particle と. That particle is no different than the と you see in と思う basically.
For example: 友達は私をトミーと呼ぶ means "my friends call me Tommy".
Or, if you want to use passive, 私は友達にトミーと呼ばれている, for example (I'm being called Tommy by my friends.. although in English you would hardly construct the sentence this way).
So to get to your sentence, that simply is:
The country of Japan is made of four big islands (that are) called Hokkaido,
Honshu, Shikoku, and Kyuushuu, and over 6000 other small islands.