-ice is a suffix of nouns, occurring primarily in words that have come into English by way of the French language (for example, 'accomplice', 'price', 'police', and 'spice'.) The original French usually spelled the words with an 'S' rather than a 'C', but when they came to English the nouns took the -ice and the verbs the -ise (for example, advise and advice, practise and practice*.)
Of course, there are also lots of examples of verbs ending in -ice; 'slice', 'voice', 'service', 'sacrifice', etc. Many of these are old-timey examples of the verbing of nouns (others were always verbs, for example 'rejoice' and 'suffice', or started as verbs, like 'splice', and then were nouned).
There is no real rule to determine if an English word should end in -ice vs. -ise or -ize, but -ice words will most often make an /s/ sound, while -ise and -ize words will often make /z/ sounds. -ize words are also more likely to be verbs, not nouns. Unfortunately, -ise words are often nouns, and/or are pronounced with an /s/ sound (promise, paradise). You just gotta learn them all individually.
So, you might be wondering why we need this suffix -- what does it do? Well, it doesn't do anything much these days, but it originally comes from the Latin suffixes -itius (masculine), -itia (feminine), -itium (neutral), where is was used to modify the meaning of nouns; servus (slave) became servitium (slavery), and came to us from the French servis as 'service' (in the sense of a religious service). Likewise, justus (just) became justitia (justice), which Old French changed to justise. Perform the old S-to-C switch, and we got justice.
* The use of practice as a verb in addition to a noun is a vulgar American corruption. It was originally practice for the noun, practise for the verb, and it still is in many parts of the world.
Webster's Third New International Dictionary, 1981