If I recall correctly, the phrase is from a private letter written by Thomas Jefferson, expressing how he personally interpreted the whole idea of "Congress shall make no law respecting religion."He thought it would be good for religious people to be free to live out their religion any way they like - in private. The government was to not meddle in a man's beliefs, only govern his action. The problem of course is that for a lot of people (myself included) religion involves actions. None of those actions are illegal, in my circumstance, but they are in others. Just look at the backlash against the healthcare law that requires all employers (including religious colleges + hospitals) to provide health insurance covering contraception. Many people - I'm not talking to the activists and the more political side of things, but individuals I know - feel this law forces them to act against what their religion requires of them. My point isn't that they're right, but that conflicts like this are conceivable. That's because religion just isn't about beliefs and what you do at home.
Speaking as a religious person I find it highly offensive to think that someone else's religion should limit my freedoms. I also think it's poisonous to religions to get so involved in politics, and obviously it's bad for society as well. (For one thing, democracies rely on citizens voting their conscience, not how someone else has told them to vote - even if that person is their bishop.) I could go on about this all night. And that's how I understand the freedom of (and from) religion: no one has the right to make someone who's not a member of their religion do something because their religion requires it. The force of law doesn't get to impose religious beliefs on people.
But separation of church and state goes much further than that. Many people in society are religious, and I personally don't think it's a bad thing if they act out that religion in a way that doesn't interfere with other peoples' rights. Rights is actually too restrictive here, because it tends to ignore how our actions affect others; Westboro may have a right to picket soldiers' funerals but that doesn't make it the right thing to do.
Religion is a big part of a lot of peoples' lives (myself included), and I'm not against our schools teaching about that part of human society. I'm also not against our legislators inviting someone to pray to unofficial meetings. I don't even think it's out of line for a religious person to say "I believe X, Y and Z because that's what my religion teaches," as part of the debate over a certain policy. The tricky thing here is we can't treat that as an actual argument. Freedom of religion doesn't mean you get the right to make others follow yours, and if you want to convince people who don't accept your particular holy text (pardon the pun) as gospel. If you want to convince other people you'll probably need to go beyond "The Bible tells me so." (I also firmly believe that people can accept the same religious values and still vote differently, for a variety of reasons; this is part of why religions shouldn't be saying "vote for this guy.")
So I can get all on board with freedom of and from religion, with all the limits that implies. (As a member of a majority religion, a lot of the limits fall on me and my Christian compatriots.) But multiculturalism - which I also believe in - says you respect who I am and let me express it in public, even if it's not like you. That's so important! I've been in situations where I couldn't speak my mind for various reasons, and it's pretty miserable. It's also hard to have genuine friendship and society there. That requires authenticity, which requires me bringing my whole self to the table.
Of course the devil's in the details. I'm not crazy about "Bible" classes in public schools, especially in areas that are overwhelmingly Christian because I think they single out non-Christians as different and make school a tough place to be, for instance. Finding that line between religious coercion and religious expression can be fiendishly difficult. But I still think it's a good line to look for. I fully respect the right of atheists and noon-Christians to express their beliefs and values in the public square, and maybe convince me they're good values if you can use logic and my own values to make that case. It just seems that turnabout's fair play here.