Caution should be taken with this one. It looks like you're still using the NIV? In this case the KJV is better. Basically the question is with this verse isolated: what/who are the former things? What exactly does it mean to be a new heaven and a new earth?
Using the NIV it's a little difficult to see, the former things are the "past troubles" from the previous verse. In the KJV it's easier to see because they translate the previous verse as "former troubles". This way the word "former" is repeated, so there's a connection there. It's more similar to the Hebrew which also uses the same wording repeated over the two consecutive verses. Imagine it as poetry. The repetition between two consecutive verses sticks out.
That he who blesseth himself in the earth shall bless himself in the God of truth; and he that sweareth in the earth shall swear by the God of truth; because the former troubles are forgotten, and because they are hid from mine eyes.
For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind.
In the Hebrew it's even easier to see, mostly because Hebrew is such a concentrated language.
אֲשֶׁ֨ר הַמִּתְבָּרֵ֜ךְ בָּאָ֗רֶץ יִתְבָּרֵךְ֙ בֵּֽאלֹהֵ֣י אָמֵ֔ן וְהַנִּשְׁבָּ֣ע בָּאָ֔רֶץ יִשָּׁבַ֖ע בֵּֽאלֹהֵ֣י אָמֵ֑ן כִּ֣י נִשְׁכְּח֗וּ הַצָּרוֹת֙ הָרִ֣אשֹׁנ֔וֹת וְכִ֥י נִסְתְּר֖וּ מֵֽעֵינָֽי:
כִּֽי־הִנְנִ֥י בוֹרֵ֛א שָׁמַ֥יִם חֲדָשִׁ֖ים וָאָ֣רֶץ חֲדָשָׁ֑ה וְלֹ֚א תִזָּכַ֙רְנָה֙ הָרִ֣אשֹׁנ֔וֹת וְלֹ֥א תַֽעֲלֶ֖ינָה עַל־לֵֽב
So, looking back at the original text identifies what is "new" about the new heavens and earth. The words match perfectly from the previous verse. It's not talking about new interpretations of scripture.