Debits and credits are the terms used to identify either an increase or decrease in an account. It depends on the type of account that you are talking about as to whether the increase or decrease is a Debit or a Credit. The first step in understanding debits and credits is to forget what your bank tells you. As they are looking at it from their point of view, when they tell you that they will "credit" your bank account (in other words, put money in your account) they are correct. However, to you it is a Debit. Here's why.
Let's start with the accounting equation: Assets = Liabilities + Equity, where Equity = Revenue - Expenses (actually equity is more than just that, but for the purpose of this ...view middle of the document...
Conversely, a decrease in an asset account must be recorded on the right side of the T, meaning that it is a Credit. Looking next at Liabilities and Equity, it is treated exactly opposite to Assets (otherwise the equation wouldn't work). Because Liabilities and Equity are on the right side of the equation, any increase in Liabilities or Equity are recorded on the right side of the T. This means that it is a Credit. A decrease in Liabilites or Equity would then be recorded on the left side of the T, or a Debit.
Now for Revenue and Expenses. Since both of these are a component of Equity, whether they are a Debit or Credit is tied into how Equity fits into the accounting equation. Think of it this way, if you made money during the year, the net effect on your Assets would be an increase, or greater Debit balance. In order for the equation to work, this would mean that Equity would also have increased, or a greater Credit balance. In order for this to happen, Revenue would have to be a Credit, while Expenses would have to be a Debit. The resulting Revenue minus Expense would give you a Credit balance, or an increase in Equity. So Revenue is always a Credit, while Expenses are always Debits.
To go back to the what the bank is telling you, here is why they are right from their point of view. They owe you money (your bank account balance). This, to them, is a Liability. Therefore, any increase in the amount they owe you would be a Credit on their books. However, to you, your bank account is an Asset. Therefore, any increase in your bank account would be a Debit on your books.