What does "keep it slow" mean?

I'm a straight male, 20 years old; I met up with a female friend yesterday. I like her and we're friends. I sent her a drunk message last Saturday admitting that I liked her and that I wanted to ask her out. She said to meet up with her yesterday and have "that conversation". Anyway, we had the conversation and the end result was that we'd give it a shot (which I was chuffed with) but that we would keep it slow as we don't want to rush into anything and ruin either the potential relationship or the friendship (her idea, I agree with in honesty). I've never been in a relationship before and have had very few "things" with girls in the past, all of which have only been one-nighters and then friends after. After she left (she was at mine) we hugged to say bye. We met up in the evening and did the same. I feel difficult to ask her but I can't make heads or tails of it. I'm not exactly expecting a full-on snog but how long am I supposed to be waiting before any contact like that? If that's if we're "going out", that is. Part of me wants to ask her about this but to me it seems a totally stupid idea, and also extremely pushy. On the other hand, is it seen a rushing things to ask her out on an actual date (e.g. dinner)? Thank you :)

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