Where are the images located which you are trying to import?
If they are on any external device, then first copy them on your computer's local drive and then try to import them into Lightroom.
If that does not help , then try to create a new catalog by File->new catalog and then try again.
What operating system and version are you running?
What exact version of Lightroom are you running?
What camera are you importing from?
Raw or JPG?
Card reader or directly connecting the camera to the computer?
What is the exact error message you are getting?
Playing a hunch, check your destination folder(s) for typos; and using Finder/Explorer, check for READ and WRITE permissions on the destination folder(s).
I am using a Mac with Lightroom 5. Importing Raw photos from my Rebel T3. The camera is connected to my computer.
I am trying to friend the destination folder but am unable to find it...where is it located? Thanks!
In the right pane of the import dialog, there is a panel for making an optional backup of the images and a panel for the primary destination.