Simple. Your web designer is trying to promote themselves by putting an advertisement on your website. My theory is that the larger this link at the bottom of the website is the worse their skills are. I’ve seen some with whole logos at the bottom of peoples sites. If you pay a web designer to build you a site and they put a link at the bottom, they should atleast ask for your approval. I’m telling clients now to go back and invoice that web designer. Charge them 99/month to advertise on your site. I bet that link goes away real fast.
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The concept behind that link. One of the ranking factors with Google is sites that link to your site. Now if you build a lot of websites and they all have links back to your site, Google will see you have a lot of backlinks. This is great for the web designer, but not so great for you. The cost to you is the loss of some of you page power. It looks like your site is linking (voting to+1) to their site. They could simply add a rel=nofollow telling Google not to steal some of your page power and don’t follow that link. This would just leave them a link at the bottom of your site though, and by itself its just tacky.

Sometimes its worked out early on where the web designer says they want to have a link on your site, and you like them for helping you out. You decide to let them put a link there, that’s fine. You should really ask the question though about will they use rel=nofollow, because you don’t want this to hurt your ranking on Google. Better yet, will they put a link to your site from their portfolio or works page? If the link is recipricol it will help both of you on Google.