Once snapshot isolation is enabled, updated row versions for each
transaction are maintained in tempdb. A unique transaction sequence
number identifies each transaction, and these unique numbers are
recorded for each row version.
What this means is that there is additional computational and storage overhead on a per-transaction basis (bookkeeping), however by adding this additional load more operations can be going on concurrently--IF they do not collide. This form of "optimistic concurrency" is one where a small performance penalty is incurred to perform bookkeeping that lets you catch when something has collided, at which point you have to unwind one or both transactions. However, if no collision occurs, then both transactions went through at the exact same time.
A poor analogy would be assume you have two transactions that would take 5 seconds individually, so to do one after another they take a total of 10 seconds. However, if you were to spend an additional second on each one, you could do both at the same time. Sure each now takes 6 seconds (a 20% penalty) but both complete in 6 seconds total instead of 10.
If you don't have really high levels of concurrency, making each transaction slightly more expensive might be a waste of resources because it would reduce your individual transaction throughput. Therefore it is something your DBA would want to consider when trading off enabling at the database level because it impacts every transaction by changing how they are stored.