What version of Lightroom?
What operating system?
What camera are you using?
Are you connecting the camera or using a card reader?
What happens when you try to read the card?
Are there any error messages?
Is this a problem with raw images or all images?
The more details you can provide, the more likely it is that you will get some help.
The version of Lightroom is 5.7.1.
The operating system is OS X Yosemite 10.10.5
I have a Canon 6D and I use a card reader.
A window pops up that says that the files cannot be read.
All images are a problem.
This message indicates that the folder you are trying to copy the photos into does not have write permission.
So, in Lightroom, determine what folder is the Destination folder (it is on the right hand side of your Import dialog box). Then go into your operating system and change the permission on this folder to write permission.