Me too! As I am a complete financial illiterate, can anybody explain if I should really be worrying about this? I've heard people say to make cost a decision factor, and others say the opposite.
It depends on what you're comparing. Most schools will give you a similar quality of education, with each school giving better access to residencies in a certain area. Top schools will let you get into the top academic residencies, and certain schools prioritizing primary care/without a lot of home departments may make it more difficult to get into competitive specialties, but for most schools there's not enough difference to justify any real difference in tuition.
AAMC has a debt calculator, and I wanted to compare Tufts vs UMass, assuming a 3 year residency.
Assuming borrowing average 95K per year for Tufts, the standard 10 year repayment plan has you paying ~$5100 a month for 10 years, for a total repayment of nearly $600K.
Assuming borrowing an average of 70K per year for UMass, the standard 10 year repayment is ~$3750 per month for 10 years, total repayment of about $440K.
If you can afford to pay $5100 on the UMass loan, you can pay it off in 6-7ish years instead of 10. That gives you ~3-4 additional years of being debt free for choosing a school with a cost of attendance about $25K lower. Relatively small differences can add up to a lot in the end, especially when looking at two schools that will give you about the same chance of matching into the specialty you want. I think cost should definitely be considered closely.
EDIT: This is kind of back of the envelope math, I'm sure someone can calculate it out much more exactly. The point is that seemingly minor differences in cost can change repayment down the line on the order of years.