This is a subject that comes up fairly regularly, and it is impossible to say that any specific amount of time or accomplishment in a lab is necessary. Also, no research accomplishments can in and of themselves guarantee that you will get admitted here or anywhere else. With those caveats, I would answer this question by saying that your research experiences should be "significant."
What does that mean exactly? Well, it will vary by the person, but I would liken applying to CCLCM to applying to an MD/PhD program. You really do need to have a research background of some type if you want to come here, along with all of the shadowing and volunteering ECs that all medical schools look for in their applicants. Most of the students in my class have spent at least a year working in a lab, and many of us have spent significantly more time than that. As I've mentioned several times already, some of my classmates even have graduate degrees. So if your research experience consists of washing glassware for a semester, I would say that this is inadequate.
That being said, no one expects you to come in here having published ten papers, either. I think if you have done an undergraduate honors thesis, or you have have taken a year or two off to do research after college, that is "significant." Also, the research does not have to be in a biomedical science lab necessarily. We have several people in our class with backgrounds in engineering, physical sciences, computers, social sciences, and ethics. So if you go to a school where you can't do biomedical research, or if you're really interested in working with a professor in a different field, then there's nothing wrong with choosing a lab in another field, or doing research in a non-science area. You should do research in a subject that interests you and that you are enthusiastic about.
One other test you can use if you're trying to decide whether your research background is "significant" is whether the professor you're working for can write you a good letter of recommendation that describes your research abilities with specific examples. If so, then again, that would count as "significant" research. But if this person doesn't even know who you are, that's not a good sign.