Firmament
The primary reason the word "firmament" has been updated in modern translation (using the term "changed" is incorrect - new translations start with the original language, not the KJV text) is because language changes. While the word was an ordinary one in 1611 meaning something like
The arch or vault of heaven overhead, in which the clouds and the stars appear; the sky or heavens. (Oxford English Dictionary)
it is now used almost exclusively in connection with the Biblical account of creation. As such, the word has taken on connotations of what people think the Bible authors meant. With such connotations often derived from ideas expressed by other Ancient Near East cultures, ideas which were not necessarily shared by the Hebrew people.
The Hebrew word in question is רָקִיעַ (raqiyaʿ; root רקע, rqʿ ). It literally means something more like "expanse" or "extended surface", deriving from the verb רָקַע (raqa) which means "to beat, stamp, or spread out". Figuratively it is used for "the vault of Heaven." (Brown-Driver-Briggs)
Heaven
The word translated as "Heaven" by the King James and "sky" by some modern translations is שָׁמָיִם (shamayim). The word usually means "sky" or "heavens", but sometimes the abode of God (i.e. "Heaven"). (Brown-Driver-Briggs)
Modern translators correctly understand that God is not creating his abode here, but rather the sky, as the context makes it clear the creation of the parts of the Earth is what is being described. The King James translators probably understood this too, but were influenced by the theology of their day which did not see a difference between the place beyond the visible sky and Heaven. Thus, they chose the more powerful word choice.
The modern understanding of Heaven not being "up there in the sky" makes "Heaven" an inaccurate translation of the Hebrew, which is clearly talking about the physical sky in some sense. (Not all modern translations have chosen to make this update, though, as "heaven(s)" can still mean "sky" in some usages.)
Verse meaning & translation
In Hebrew, then, verses 7 and 8 are basically saying God created the sky-like stuff and called it sky, but it a much more elegant way. Translators are tasked with translating this in an intelligent way that both retains a distinction between the creation action and what the creation was then called and uses sufficiently elegant language. In 1611, firmament was a good choice because it was a normal, semi-poetic word for arch of the sky. In 2015, firmament is a poor choice because the word is mostly archaic and has connotations that the Hebrew does not support. Thus, translators have variously picked "expanse," "vault," or "space" to express the idea conveyed in the creation act, believing such words capture the idea without the confusing (to a modern reader) use of an archaic word.