Balance Forward
A Balance Forward is the previous balance on an account that has been carried over from the previous statement to the current statement.
For example, if a tenant did not pay their rent last month and owes you $1500 ... the balance forward on their current statement would be $1500 because they still owe you that money: 
Another example would be a bank account ledger. Let's say the balance on your bank account at the end of 2018 was $25,150.25.
If you view a statement for 2019 dated from 01/01/2019 - 12/31/2019, the Balance Forward by definition would be the previous balance ($25,150.25) which has been carried over from the previous statement to the current statement:
The only way to remove a Balance Forward is to "include all dates" on the current statement so that there is no balance to carry over from a previous statement.