As well as emphasizing that it happened some time in the past, back in 2003 has a more informal feeling to it than “in 2003”. If you have an official document from 2003, don’t refer to it. No copy. On the other hand, “in 2003” may sound a bit too calculated for a casual conversation; adding ‘back’ adds additional information about how you feel about how far away that time was, so it comes across as friendlier. I see the reference to this in the paragraph last paragraph. If I look at ‘we

started our company back in 2003′ on

a company’s website, for example, You might find something like

We started our company back in 2003.