I would say, this is the most confusing property in the Microsoft SQL Server. Most misunderstand it and most do not know how it works. Although there are many posts on this, only few explains it with an example, and some articles/posts make it more confused, hence making this post the way I understand;
If you refer MSDN, it explains it well but in simple term, what it says it, if you set an expiry date for your backup set (if you need to understand what is backup media set, backup media family, backup device or backup set, read this) or if you set Retention days, the backup set can be overwritten only when the backup set is expired or after number of days mentioned with Retention days (this is shown as After x days in GUI).
Simply, if I take a backup today (19-Mar-2017) and set the expiry date as 25-Mar-2017, I will not be able to overwrite the backup set until 25-Mar-2017. Remember, backup can be restored any day regardless of the expiry date set.
Here is an example;
Let's take a backup of AdventureWorks2014 database. See both ways; using GUI and TSQL. Note that I have mentioned a name for Media too. Without this, expiry setting will not as we expect.
BACKUP DATABASE [AdventureWorks2014] TO DISK = N'E:\DatabaseBackups\AdventureWorks2014.bak' WITH EXPIREDATE = N'03/25/2017 00:00:00', FORMAT, INIT , MEDIANAME = N'Media01', NAME = N'AdventureWorks2014-Full Database Backup' , SKIP, NOREWIND, NOUNLOAD, STATS = 10 GO
Now if you try to take another backup to the same media by overwriting the existing backup sets;
BACKUP DATABASE [AdventureWorks2014] TO DISK = N'E:\DatabaseBackups\AdventureWorks2014.bak' WITH NOFORMAT, INIT , MEDIANAME = N'Media01', NAME = N'AdventureWorks2014-Full Database Backup' , NOSKIP, NOREWIND, NOUNLOAD, STATS = 10 GO
SQL Server will throw this error;
If you still need to overwrite it, with TSQL, you can use SKIP instead of NOSKIP, or with GUI, do not mention the Media name.