That's so nice of you.
Εσωτερικός comes from the ancient greek έσω, which means inside, μέσα. (the other part is a basic adjective part. There's no etymology for it to be found.)
The opposite adjective is εξωτερικός, and comes from έξω, which means outside, έξω. ^.^
Also, interesting are the prefixes/prepositions εισ- and εκ-. But it would take A WHILE to explain all the possible uses and meanings of those two.(When you have a great amount of free time, I could do the honors and bore you to death with such etymology stuff.)xD
To add to this, I think that the adjective ending is -ικό(ς), and the -τερ- part is usually used to construct the comparative of adjectives and adverbs, quite similarly to the -er in English, for example:
- νέος = new, young, νεότερος = newer, younger
- ωραίος = nice, pretty, ωραιότερος = nicer, prettier,
- (π)άνω = up, above, ανώτερος = superior, etc.
Εσώτερος and εξώτερος exist as words, though they are too formal-scholarly I think, and mean "inner" and "outer" respectively. In particular, the phrase "το πυρ το εξώτερον" means "the fire of hell" (πυρ = fire in ancient Greek) and it is the most usual way to use this word. On the other hand, εσωτερικός and εξωτερικός are everyday used words and don't have any comparative meaning, despite their origin.
Another adjective created similarly is νεωτερικός.