Users below 15 reputation can't effectively vote. It says:
Votes cast by those with less than 15 reputation are recorded, but do not change the publicly displayed post score
Does it mean that they will take effect after I reach 15 reputation or because they were cast before, they're recorded but ignored?
They aren't ignored, but they won't change the post's score (or the reputation of the poster), not even after reaching the required reputation for upvoting. It works the same way as downvoting with less than 125 reputation; your votes are stored as 'feedback' but it is not entirely clear (at first sight) what's done with it. It turns out that this feedback is visible in the moderator tools available to 10k users, and in the Stack Exchange Data Explorer.
After you reach 15 reputation, you need to upvote the post (again) and then it will affect the score.
Update: The message has been changed to make it clearer that you're not actually casting a vote if you don't have enough reputation to do so.
They are not ignored, they just have different effects. The votes are viewed as "anonymous feedback" per site which is only viewable when you get access to the moderation tools privilege at 10k rep on that site or 2k if the site is in beta.
Since they are counted this way, they will not automatically convert into actual votes when you gain the privilege.
