This is essentially a Correct Horse Battery Staple approach to password generation, with a twist to make passwords more concise and easier to type.
The words are selected from a wordlist included with the Bitcoin Improvement Proposal #39. The wordlist consists of 2048 common English words, such that the first four characters of each word is unique. This website simply selects five random words from this list, which allows you to safely skip all characters after the first 4 for more efficient password typing.
The page can generate 35853175596564480 unique 5-word passwords, for about 55 bits of entropy. Assuming you pick your favorite of the 16 given here, that lowers it to 51 bits.
Note that a good password is not enough to keep you secure.
The best password is no password at all; many pages allow you to login with your account from Facebook, Google, or some other provider. This is more convenient and more secure than coming up with your own password.
The second best kind of password is a random password stored in a secure password manager. Most major browsers come with one now. You should use it.
Finally, for the few accounts where you do want a password you remember, always use 2-Factor Authentication as well. This is the biggest thing you can do to keep yourself safe.