Confused about wireless passphrases vs. keys

For historical reasons my WPA-PSK-TKIP
password is 10 hex characters generated from
a couple of dictionary words concatenated.
I went to this site to check my password:
http://www.passwordmeter.com

According to their algorithm, my concatenated
words are very weak, but my 10 hex digits are pretty strong.
Let's NOT argue about their test method. My question
is simpler than that.

There's a box in my router where I type the
"WPA shared key".
I put in the 10 hex digits.

In my pda, it's called "Network Key".

In some devices, it's called "passphrase".

I don't understand how a dictionary attack works.
Does it start with dictionary words and test keys
generated from them? Or does it test the words
directly?

So, is my network insecure against dictionary attacks
because I started with dictionary words?
Or is it much more secure because I put the hex digits
in the key field?

I don't have anything critical unencrypted on my network.
I'd just like to keep out casual explorers.
I really don't want to learn a new huge key if I don't have to.

Thanks, mike