The Reputation Score is basically the way Steemit measure the value you have brought to the platform. When you first start on Steemit you have a Rep Score of 25 and this number can go up or down depending on how users upvote or flag your content.
Each level of reputation is 30% harder to reach than the previous level. For about 8 months I seem to have been stuck on Reputation Score 59 so I'm really happy to have finally reached this milestone!
The number is important because some Steemit users will read posts from people with higher Reputation Scores as there is a greater chance of finding high quality content, because the user has been 'vouched for' by the community.
For me to hit 60 Rep I had to accumulate a total value of 7,742,636,826,811 vests. The next level of 61 will be 30% harder to reach so I will need to reach a vesting score of 10,000,000,000,000.