• sudo is telling the computer to do this with root privileges.
• chmod sets permissions.
• Each digit of that three-digit number corresponds to the owner, the group, and other users, respectively. It's 0–7, where 0 means no access and 7 means access to read, write, and execute. So 077 is the exact inverse of 700, where 077 means "the owner cannot access their own files, but everyone else can read, write, and execute them". Corresponding 700 to asexuals is joking that nobody but the owner can even so much as touch the files.
• / is the root directory, i.e. the very top of the filesystem.
• The -R flag says to do this recursively downward; in this case, that's starting from /.

So here, we're modifying every single file on the entire system to be readable, writable, and executable by everyone but their owner. And yes, this is supposed to be extremely stupid.

7 is read, write, and execute permissions. 700 is owner, but not group or others. 077 means the owner has no permissions, but group and others all have full permissions.