The first 10 GB of storage is free. As of early 2016, the price is $0.005 per GB per month, after you exhaust the free tier.
The first 1 GB of download per day are free. As of early 2016, the price per 1GB of download from your stored data, will be charged $0.05 per GB.
A 'transaction' refers to any time an api call is made with your account, such as listing the contents of your bucket or downloading a file. B2 will charge for some transactions however, for the average user, these charges are largely negligible unless you are making an extremely high volume of api calls.
Class A transactions are free.
The first 2,500 Class B transactions are free each day. As of early 2016, additional Class B API calls are charged at $0.004 per 10,000 calls.
The first 2,500 Class C transactions are free each day. As of early 2016, additional Class C API calls are charged is $0.004 per 1,000 calls.