When you first create your account you start at a reputation of 25 and your reputation will increase or decrease based on the upvotes or downvotes you receive.
Digging a little deeper:
The reputation system is a piece of data that allows the network to communicate the "trust-worthiness" of any given member within the network, the system does this through a plugin running on the network that looks at a number of metrics.
Raw reputation on the blockchain is actually stored as a record of the total amount of rshares that have been recieved by any given account. What that essentially means is that it records the amount of times you have been voted for (on any of your posts or comments) and how much steem power each of those accounts had behind them (or to be more explicit the percentage of voting power of the total steem power of each account which voted. )
Posts talking about reputation:
An excellent explanation on calculating reputation level (which is the number displayed on steemit.com and on esteem as well as on busy.org) from raw reputation can be found here:
An interesting glimpse into early iterations of the reputation system can be found here:
Nate Brune (@picokernel) discussing the reputation system:
Where to find reputation:
You can also find your raw reputation on steemd.com by browsing to steemd.com/@yourusername
Raw reputation calculation on ruby on rails
Network Reputation Level: <% raw = @account.reputation.to_i %> <% neg = raw < 0 %> <% level = Math.log10(@account.reputation.to_i.abs) %> <% level = [level - 9, 0].max %> <% level = (neg ? -1 : 1) * level %> <% level = (level * 9) + 25 %> <%= number_to_human(level) %>
Calculations thanks to @inertia and also require Radiator(obviously)