My mom works at a company that I am applying to and I'm going to be applying there soon. Would it be a bad idea for her to give me a referral? I understand it comes off as being biased, which is why I'm thinking that it might be a bad idea.
As with all referrals, there's a credibility in function and a credibility out function.
A referral from a parent who is him/herself highly credible in the organization is likely to be respected to some degree. If I know you do very good work; honestly look out for the company and team's best interests; never compromise on quality; treat everyone with respect regardless of your personal relationship; view issues objectively; and so on — I'm likely to take your description of your son or daughter seriously.
If, on the other hand, you take a somewhat lackadaisical approach to your own work; you often blame others for issues; your ideas about whether or not an idea will work are often inaccurate or biased; you haven't invested in relationships with your team; and so on — I'll probably shrug when you tell me how great your son or daughter is.
That's the credibility in function. If it's high enough, an interview might take place. The credibility out function, then, is how much said son or daughter goes on to fulfill expectations. Hence, as Kilisi said, if you are hired, make sure your conduct and conscientiousness proves your mom right.
My aunt works at a large property development firm. She was headhunted from a previous firm where she had done great work. At the new firm, she quickly confirmed her reputation as a serious and competent employee. Her son, my cousin, just finished an undergrad degree in mechanical engineering. She asked her manager to take a look at his résumé. The manager, knowing his mom to be a trustworthy person, agreed after some insistence. He turned out to impress the manager in the interview, so they hired him.
It's fine so long as she lets people know about the relationship. A referral which has "this is my son, I think he's great" lets people know that she might not be entirely unbiased.
A referral which says "jerry is the best young person I've ever met. I would wholeheartedly recommend him for his role, and recommend an immediate pay rise" without mentioning the relationship is deliberately concealing important information and is not ok.
When a company sets up a system where current employees can refer people they know, they are trying to find a way to get quality candidates. They may be good because you have worked with them for years. They may be good because they have similar work ethics.
Not everybody recommended will be hired. Not everybody recommended will be a good candidate. It is Ok to recommend a family member. In almost every case the recommendation comes with bias. The two people know each other. Nobody believes them when they say this person is the best underwater basket weaver in the world. They are just their favorite currently unemployed basket weaver.
Now if the company is small they may have a policy about hiring family members at all. Even big companies may not allow family members work too close together. So it is possible that this recommendation may not go anywhere.
I once hired someone in an American public sector position and it almost got derailed when she told HR that one of her references was her cousin. He was in an appropriate position to give her a recommendation, professionally (being in a line of work that matched the job we were hiring for), but there are anti-nepotism laws and policies in many places, and sometimes they're not clear until the end of the process.
Referrals aren't references, but the policies might apply.
I would recommend finding someone else to give the referral, but being open, if you're hired, about your mother being an employee (nothing wrong with it as long as she didn't influence the hire.)
It is okay if you make it transparent. That is not to just repeat Philip Kendall's answer - she is an adult and she stakes her professional reputation on that referral. If you turn out to be an entirely unfit candidate and it actually wastes company resources as opposed to grabbing your average Joe from the streets, it will be on her. Past that, it depends on the country/culture a lot: there are places where entertaining some light nepotism is considered okay or even virtuous (hiring young relatives to give them job experience for better-than-McDonald's pay but still acceptably low for an entry position). Crucially, in this scenario it is your mother who has her reputation at stake and who has made this decision. You are entering this arrangement basically risk-free. Respect her decision and her help and you will be fine.
Would it be a bad idea for her to give me a referral?
YES, very bad idea.
Your mother is clearly biased (as she darn well should be). A reference from her can't be viewed as an objective assessment and hence it's useless for the interviewer.
Providing a reference from your mother would be very tone deaf. It can very well be interpreted as "this candidate is still being helicoptered by their parents".
Keep your personal/family life separate from your professional life.