Colonial Offices is a good Diplomatic Policy to enact if you are an expansionist nation which likes to spread to faraway lands. A 15% growth boost isn't negligible, and could spur the growth of new cities considerably. But remember that this will be nearly useless without the proper Housing infrastructure. Also keep in mind that the policy will act only for cities not on your original continent, and not for all cities! Thus, if you are a small empire, and haven't had the chance to spawn near the fault line of two continents, Colonial Offices will be useless to you.
Once national governments began taking a hand in (and taking over) overseas colonies founded by trading companies, military adventurers, and religious fanatics, the ad hoc administrations of such distant outposts needed a firmer hand. Thus, the Spanish formed colonial offices, and were soon emulated by the other colonial powers. In the late-1500s AD the Spanish monarchy formed the Council of the Indies (although it didn’t assume its final form until a century had passed), a hierarchical organization to rule over the colonies since the king couldn’t be bothered. Initially two viceroyalties were established (two others later); Spanish viceroys had judicial and legislative control of their territory, and – more importantly – had direct access to the colonial treasury.