to load = to log in?

[NewHopeR]

Context:

“The fact is that the vast majority of Mega’s Internet traffic is legitimate, and we are here to stay. If the content industry would like to take advantage of our popularity, we are happy to enter into a dialogue. We have some good ideas. Please get in touch,” the company said.
MegaUpload boasted “more than 150 million registered users, 50 million daily visitors and accounting for four percent of the total traffic on the Internet,” according to the Justice Department, whose website was also unable to load, at the start of this writing. According to Twitter user AnonymousIRC, a highly-popular account related to the hacktivist group ‘Anonymous,’ the DoJ’s website appeared to have been “besieged by pirates.” It is unclear at this time whether Anonymous had anything to do with the outage, which has since been resolved.

[Shenfeng]

Hi,

when a website loads it means that it is working, that you can see and interact with it.

It's called "loading" because the web browser has to load the website's various files (HTML, CSS, scripts) from the server down to your computer and process them. After all that has happened without any major errors, you can actually use the site and it is "loaded".

Edit:
If some people were to bombard the website's server with a huge number of connection requests, the server would pretty soon reach a point where it can no longer reserve any more memory for those requests and eventually break down with the result that the website would no longer able to load (the server wouldn't respond anymore), because the server wouldn't be able to send those HTML, CSS and script files anymore.

[BobSmith]

whose website was also unable to load

is later explained with

had anything to do with the outage

[not a teacher]

to load = to log in?
No, not exactly, in this case.

See also Denial-of-service attack.

[NewHopeR]

Thank you both