Like the person the my right said, miles indicate how much it has been used. The higher the use the more that will be needed to fixed. Not only do the miles themselves matter, but also what type of miles. I would rather buy a car that had 250,000 miles of highway over a car that had 100,000 miles of city. It's harder on the vehicle. It also depends on the vehicle itself.
The important part here when buying a car for me is the condition it is in, I don't even care about the mileage, however, I will use it to determine what to look for when looking for problems.
I always check for rust, body damage, excessive wear, missing or damaged engine components, maintenance records, and practicality of repairing any found problems before even considering the mileage.
You could have a low mileage vehicle that looks great, but may have underlying problems that will be hard to spot from the surface. It could have been used primarily on salted winter roads and sat the rest of the year. It could have been totaled and salvaged to rebuild and sell. It might have city miles as opposed to highway miles, and city miles mean more wear and likelihood that its been in a fender bender. Vehicles with irregular oil changes, low oil, or an oil pressure problem are obviously going to have more wear in a much shorter distance than a vehicle with a properly maintained oil system.
We had a truck that was literally falling apart at 29,000 miles because it was only driven in the winter where the salt gets on everything. I recently bought a convertible which currently has 122,000 miles on it, and has no structural or safety compromising damage. That convertible was garage kept, and maintained very carefully. I did an engine repair on it and the inner workings of the engine were like new!
Mileage is still important to consider, but don't let it be the only deciding factor.
Any vehicle can last a lifetime but if its not maintained during its scheduled maintenance then it will have expensive problems down the line. Miles indicate how much the vehicle has traveled and indicates how much its been used, just like any other machine your going to have to care for it if you want it to last.