This is a great phrase that can be used in both spoken and written English. If something looks good “On paper” it means that all the information you have seems like the situation would be great. What is good “on paper” and what is good “in reality” are often 2 very different things. Here are 2 good examples.
The L.A. Lakers are a great basketball team on paper. It is their first year playing together though so they might not play as well as people are expecting.
(That means, there are a lot of great and famous individual players on the team, so it seems like they will perform very well. They look good on paper. The reality is, however, the team may not play very well as a team.)
Another example:
That couple seems great on paper, but I heard their relationship isn’t going very well.
(This could be something like, the guy has a good job, a good education, he is tall, kind, and good looking. The girl is beautiful, she is well-educated etc. They both like to travel and the both like cats.)
That sounds like a good relationship “on paper“. It doesn’t mean they will be happy together in reality though.