Data remanence is the term used to describe the remnants of data that are left on a machine such as a computer after the data has apparently been deleted or erased. Not all data erasure methods will actually permanently delete data and this data will leave traces (i.e. the data remanence) on the machine in question which allows specific types of software programs to recover it.
So, for example, if you are working on a Word document on your computer and decide to delete the file because you do not need it anymore then you might well think that the file has been wiped from your machine. The truth is that the standard delete function (and many other types of deletion/erasure) does not actually remove the file permanently. Basically these functions will remove any pointers to the Word document in your system so that you cannot find it. But, a software retrieval program could well find it as it still there behind the scenes.
In most cases data remanence is not an issue. Having your Word document behind the scenes may not be an issue to you but, if it contains sensitive data, then this could be a problem in some cases. So, for example, if you then sold on your computer to somebody else they could use software to recover the data that you think that you have deleted once and for all and access your information.
There are many solutions to data remanence. These include software programs that will wipe or overwrite data, disks and hard drives to make sure that deleted and indeed other files and data are permanently removed.