Assuming bbb doesn't occur after the text you are interested in, and the reverse constraint for ddd, you can do it like this:
sed 's/^.*bbb //; s/ddd.*$//' <<< "aaa bbb ccc ddd eee"
Output:
ccc
sed is probably not the best tool for this, maybe you could explain a bit more about what you are trying to do? For example you may want to use positive lookbehind and lookahead:
grep -oP '(?<=bbb ).*?(?=ddd)' <<< "aaa bbb ccc ddd eee"
Output:
ccc
Edit
According to comments the OP wants to extract the ip address from checkip.dyndns.org. A generic and more portable way to do that is with grep -o, e.g.:
curl -s http://checkip.dyndns.org/ | grep -oE '([0-9]+.){3}[0-9]+'