Question about wisdom teeth?

Last time I went to my dentist for a routine cleaning the hygienist and dentist both mentioned the possibility of removing my wisdom teeth at some point as they haven't came in. Their words were "Unless your teeth do some shifting we'll probably remove them". It seems like i have room for them, and they said "They don't look like they'll come in on their own". So what exactly does that mean? If they don't come in on their own is it absolutely necessary to have them removed? What would be my options/consequences for not having them removed? I'm also wondering if they are starting to come in or if my teeth are shifting like they mentioned because I had a pain in my mouth today (never a cavity and always healthy teeth) but I started having pain on my right side of my mouth, then left, it was in the gums and towards the back of my mouth, mainly on the lower jaw?