According to this text: http://prawo.vagla.pl/node/9637 (in Polish, from a lawyer who is against ACTA), there was no real attack on any of the mentioned sites, it was just that there was so much interest in the case that some sites went down due to naturally increased traffic. Case in point: his own website went down, even though he is against ACTA.
Well, so let's be more specific about the alleged attack.
1) At least one target was attacked quite literally. The website of the Polish Parliament was defaced and subsequently taken down by its admins.
[This is the supposed deface image: http://bit.ly/wkygL4. The caption reads "Nothing is impossible! Cheers, gentlemen!"]
2) ACTA is a very new thing to the wider public (even the "trendy" internet public). First, on Jan 20 it made the front page of the biggest newspaper of record, Gazeta Wyborcza. And today ACTA was mentioned in the main TV news program (Wiadomosci on TVP1). The latter almost certainly triggered a wave of searches and attempts to access various sites. In result many website failures (the lawyer's, the Panoptykon Foundation, perhaps even Ministry of Culture) can be attributed to a sudden spike in interest.
[The lawyer mentioned in previous post has stated specifically that he has investigated the nature of the traffic and it doesn't look like a DDoS. Which is kind of credible, since each machine participating in a DoS sends gazillions of requests from the same IP, so it's distinctive from a visitor sending like 5 requests in total.]
3) That said, it's not an outlandish assumption that someone also had their way with the biggest sites of the Polish Government. A DDoS could have contributed to the whole mess.
The simplest way is to use netstat and check amount of connections from each host. If you see plenty hosts with many connections established, that's DDoS. If there is plenty hosts, but each one has few connections, thats DoS (aka slash dot effect), mentioned by Tomek_.
PS: DDoS - distributed denial-of-service attack. Deliberate attack which involves dedicated software; DoS - denial-of-service. Server can't handle all requests, because suddenly there is more of them (because of link on frontpage etc)
