Trying to understand how a website is getting higher than me with less links

[ClaireH-184886]

Hi i am new to seo and trying to teach myself the best way to improve a site and the best way to use the tools on seomoz.

The problem i have is. i am working on a page at the moment on a site. the page is called weight loss hypnotherapy http://www.clairehegarty.co.uk/weight-loss-hypnotherapy and i have around 130 links going to the page where as a site which is much higher than me in google has only around 5 links.

I cannot understand with being new to seo how this can happen, can anyone please explain what i need to do to improve my ranking please.

here is the site i am talking about that is higher than me www.weightlosshypnotherapy.co.uk/

any help would be great

can anyone also give me a good example of a page before it has been optimised and a page after it has had this done.

[mypctechs]

I was thinking of the same exact page to post in reply when I scrolled down to find that you'd already posted it. This is dead on.

I absolutely can't wait for search engines to stop placing so much emphasis on domain keywords. I can't tell you how many times I get the dead fish stare from a client when they learn that their business name that they've had for 25 years is NOT the best domain name for their business website.

[SteveOllington]

You'd do well to study this a bit http://www.seomoz.org/article/search-ranking-factors#metrics-1 

It has many answers to your Q.

[Devonlad]

The age of the site and authority of the site is also very important. If your competition have an old site and the five back links are of a really high quality, that may very well outweigh  your back links. However, if the site is well respected and old, has great content and offers visitors the answers to their search combined with keywords in their URL, they will be very strong!

[EGOL]

i have around 130 links going to the page where as a site which is much higher than me in google has only around 5 links.

It's not how many you have.  It's their quality.

PeterM22 points to another good reason - there KW domain is exact match.

[PeterM22]

One possible reason is that weightlosshypnotherapy.co.uk is an exact match domain. The keywords are in the domain name. Google tends to rank these domains much higher, all other things being equal, especially if they are aged exact match domains.

Hope this helps