Here’s what Andy has to say about them:
For those of you who have not come across this feature of Oracle, it was introduced in 9iR2. It allows you to set up your session so that if a transaction hits a storage problem e.g. out of temp, tablespace is not big enough,or a table reaches max extents, the transaction is suspended. All you have to do is fix the space problem and and transaction will resume. This saves you all the time of waiting for the rollback, adding some space and starting again hoping you’ve got it right this time.
He goes on to explain in great deal how to setup for and use resumable transactions. I didn’t even know you could do this (damn lack of training budget.) Great article Andy!