The word afterwards means subsequently or later on. For example, a couple may have sex and then continue their endless bickering afterwards. Lucky couple, except for the bickering part.
For some reason, The New Penguin English Dictionary (1986) lists the word afterwards, but not afterward, yet the two can be used interchangeable.
It’s not just me who believes that. I checked with the thesaurus bundled with Mac OS X. It lists afterward and afterwards as synonyms.
I don’t know why the Penguin dictionary omitted afterward. Maybe it was a mistake. I haven’t seen any editions of the dictionary beyond the 1986 one that I have on my bookshelf. Maybe they added afterward afterward. Or maybe they added it afterwards. Whatever.