DoninGA is correct that this is usually a problem where the Social Security Administration has passed to the IRS a database and the information (name and SSN) on the tax return doesn't match any entries in the database.
One common cause for this is that the taxpayer married and never notified the Social Security Administration of the change of name. Thus the taxpayer uses the married name on the tax return but the SSA still has only the original name. Note that it takes months for the change to migrate through the SSA and over to the IRS, so changing your name at the SSA and shortly thereafter filing your return will often cause this mismatch.
One way to test this is to change the name on the tax return back to the original name and re-efiling; if it goes through, then this was the problem. Note that a refund will be paid to the original name, so you want to make sure that your bank knows you under both names.
Note that in some cases, this can be caused by the Social Security Administration misidentifying the taxpayer's "last name". This can happen with certain ethnic groups who have multiple names.
For example, take the name María González García. In the traditional Spanish naming convention, González would be the last name of the father's side and García would be the name of the mother's side, but in recent times, some people have been switching the two names. A taxpayer with this name might reasonably think that her father's last name (the second word) is her last name and use it on the tax return, but the Social Security Administration might have recorded García as the last name. Or vice versa (i.e., the SSA has only González and not García at all).
You can test this by changing the order of the name on the tax return so that it would be María García González and re-efiling the return, to see if the return is accepted. When I did retail taxes, this frequently corrected the "error" for Hispanic clients. Again, you have to be sure that the bank will handle the direct deposit or the refund check under either name.
Or, of course, you can do as DoninGA suggests and just print and mail your return. In this case, the automatic check to the database is bypassed, and the return will (likely) be processed.
Even if you are able to e-file, you might want to visit your local SSA office or call them as DoninGA suggested and see what it would take to get the name updated or the order corrected in their database for next year.
