There might be several reasons for this problem.
Maybe the partitions are mounted read-only, which is the default for NTFS partitions as far as I remember. If you're using NTFS, see https://help.ubuntu.com/community/MountingWindowsPartitions for how to mount them read-write.
For other file systems you can have a look inside the file /etc/fstab. Documentation about how entries in this file should look like could be found at https://help.ubuntu.com/community/Fstab. But be careful if you modify this file, you might loose access to your filesystems completely.
Another reason could be that you're not granted the rights modify files on the partition. Open the partition in Nautilus file manager and choose File -> Properties -> Permissions. If this folder is not owned by you or your group, change the ownership or give 'others' write permissions.