The first 10 GB of total storage is free and is $0.005 per GB per month for additional storage beyond 10 GB.
The first 1 GB of downloads per day are free. The price to download stored data costs $0.01 per GB beyond the free daily 1 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. 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. Additional Class C API calls are charged is $0.004 per 1,000 calls.
The pricing page for B2 is available here.
Each B2 API call is broken down by class and associated costs here.