Historically, of course, the main target was initially Romanism, and then by 1689 Anglicanism. The preface to the Book of Common Prayer declares that "the particular Forms of Divine worship, and the Rites and Ceremonies appointed to be used therein, [are] things in their own nature indifferent, and alterable" (my emphasis). Here is a different understanding of the regulation of worship, as made explicit in Article 34: "IT is not necessary that Traditions and Ceremonies be in all places one, and utterly like; for at all times they have been divers, and may be changed according to the diversities of countries, times, and men's manners, so that nothing be ordained against God's Word" (my emphasis). Where the Reformed sets forth a positive RP (only what is commanded), Anglicanism holds a negative RP (anything that is not forbidden).
What the two versions of RP have in common is that they are seeking to have worship that is regulated; that is to say, worship that is ruled. Our approach to God and the service which we offer him is not to be derived arbitrarily from our brains. We are not free to do as we please; rather, we are free to do what pleases God - which service is true freedom.
As an aside, it interests me that there is a parallel here with the differences over church government which exists between Anglicans and Reformed. The Reformed insist that there is one Biblically mandated way to organise and run a church - although they will disagree over whether this is a Presbyterian or Independent model. The Anglicans, on the other hand, will tend to say that no such Biblical model is given, and that within certain bounds churches are free to organise and run themselves as they see fit (with the proviso that catholic tradition should play a major part in the decision making process).
My sympathies are with the Reformed vision for regulated worship. What we may do is what we must do; we are free to do what we are commanded. As with the question of church government, what is at stake is our understanding of how Jesus rules his Church. To my mind, the Reformed RP makes it far more clear that Christ is active in the rule and direction of the churches here and now by his word and Spirit. Not only in doctrine, but in the liturgical actions that we take together on a Sunday, we are to be moved and directed only by him.
Having said that, I have some questions to put to the Reformed RP, which will end up meaning that I disagree strongly with the letter of it. But of that, more later.