What is the purpose of changing the default SSID?

Changing the Default SSID would serve no particular security purpose where it's not entirely predictable (e.g. 'netgear'). It would allow you to easily identify your wireless network though, if there are lots of others about.

It used to be the case where companies used one string for all their APs that it was relevant to Rainbow table generation (more info here) as the SSID is involved in generating the key (details here)

It could be that the articles you read were confusion the idea of changing the SSID with the idea of changing the Pre-Shared Key.

Changing the PSK can be a good idea, in case there is a problem with the methodology used to generate the first one being predictable (IIRC this has been a problem with some makes of access point in the past).

Also changing the PSK periodically can be beneficial if you're worried about someone brute-forcing the existing one or your worried about someone who has had access to the network and should no longer have it (e.g. in a company set-up where someone leaves the company)

For some routers, the SSID will identify the type of router (one example). This gives potential attackers more information about your network that they can use to break into it. Thus, changing the router name hides that information from the attacker. Some things that knowing the type of router can enable is finding default passwords for that router, or knowing specific attacks that will work against that router.