I had a low lying placenta at my 20 week scan. I have another scan on Thursday to make sure it has moved up. The main issue is that if it is too low, and particularly if it is covering the cervix at all, then baby is going to have trouble getting out! My mw told me that 90% of the time they move up on their own as the uterus grows but if not a planned c section may be needed.
Try not to google as there are so many awful horror stories but actually it rarely causes problems. Your scan report should also say whether the placenta is covering the cervix or not. It will say something like 'clear of os' or 'partially/completely covering os'. If its clear of the os then the chance of bleeding is low. I panicked a bit because the Internet seems to suggest you have to be really careful like no sex, no lifting etc but when I asked my mw she wasn't concerned at all and basically said to carry on as normal xxx