Repaying a loan is a type of cash outflow. Why should I care which part of each payment goes towards the interest and which part towards the principal? "A loan is a loan", no?
I know that this breakdown is considered when calculating income tax, but is there any other significance?
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The breakdown between how much of your payment is going toward principal and interest is very important.
The principal balance remaining on your loan is the payoff amount. Once the principal is paid off, your loan is finished. Each month, some of your payment goes to pay off the principal, and some goes to pay interest (profit for the bank).
Using your example image, let's say that you've just taken out a $300k mortgage at 5% interest for 30 years. You can click here to see the amortization schedule on that loan. The monthly payment is $1610.46.
On your first payment, only $360 went to pay off your principal. The rest ($1250) went to interest. That money is lost. If you were to pay off your $300k mortgage after making one payment, it would cost you $299,640, even though you had just made a payment of $1250. Interest accrues on the principal balance, so as time goes on and more of the principal has been paid, the interest payment is less, meaning that more of your monthly payment can go toward the principal.
15 years into your 30-year mortgage, your monthly payment is paying $762 of your principal, and only $849 is going toward interest. Your principal balance at that time would be about $203k. Even though you are halfway done with your mortgage in terms of time, you've only paid off about a third of your house.
Toward the end of your mortgage, when your principal balance is very low, almost all of your payment goes toward principal. In the last year, only $513 of your payments goes toward interest for the whole year.
You can think of your monthly loan payment as a minimum payment. If you continue to make the regular monthly payments, your mortgage will be paid off in 30 years. However, if you pay more than that, your mortgage will be paid off much sooner. The extra that you pay above your regular monthly payment all goes toward principal.
Even if you have no plans to pay your mortgage ahead of schedule, there are other situations where the principal balance matters. The principal balance of your mortgage affects the amount of equity that you have in your home, which is important if you sell the house. If you decide to refinance your mortgage, the principal balance is the amount that will need to be paid off by the new loan to close the old loan.
It's important because it shows that the amount you owe does not decrease linearly with each payment, and you gain equity as a correspondingly slower rate at the beginning of the loan and faster at the end. This has to be figured in when considering refinancing, or when you sell the place and pay off the mortgage.
It also shows why making extra payments toward principal (if your loan permits doing so) is so advantageous -- unlike a normal payment that lowers the whole curve by a notch, reducing the length of time over which interest is due and thus saving you money in the long run. (Modulo possible lost-opportnity costs, of course.)
Yes, the distinction between how your funds are applied to principal vs interest is very important. The interest amount charged each period (probably monthly) is not just one fixed sum calculated at the origination, but rather is a dynamically calculated amount that changes each period relative to how much principal is remaining (amount you owe).
The picture you posted showing principal and interest assumes the payer always paid their minimum payment and never made any extra payments of principal.
Take a look at the following graph and play around with the extra payment fields. You will see some pretty drastic differences in the Total Interest Paid (green lines) when extra payments are made.
The other answers have touched on amortization, early payment, computation of interest, etc, which are all very important, but I think there's another way to understand the importance of knowing the P/I breakdown.
The question mentions the loan payment as "cash outflow". That is true, but from an accounting perspective (disclaimer: I am not an accountant, but I know enough of the basics to be dangerous), the outflow needs to be directed to different accounts.
The loan principal appears as a liability on your personal balance sheet, which you could use, for example, in determining net worth. The principal amount in your payment should be applied to reduce the liability account. The interest payment goes into the expense account.
Another way to look at it is that the principal, while it does reduce your cash account, can be thought of as an internal transfer to the liability account, thus reducing the size of the liability. The interest payment cannot.
Aside: From this perspective, the value of the home is an asset, and the difference between the asset account and the loan liability account is the equity in the house (as pointed out in different language by the accepted answer). Of course, precisely determining the value of an illiquid asset like a house at any given moment pretty much requires you to actually sell it, so those accounts are hard to maintain in real-time (the liability of the loan is much easier to track).
It's important because you may be able to reduce the total amount of interest paid (by paying the loan faster); but you can do nothing to reduce the total of your principal repayments.
The distinction can also affect the amount of tax you have to pay. Some kinds of interest payments can be counted as business expenses, which means that they reduce the amount of income you have to pay tax on. But this is not generally the case for money used to repay the loan principal.
The reason it's broken out is very specific: this is showing you how much interest accrued during the month. It is the only place that's shown, typically.
Each month's (minimum) payment is the sum of [the interest accrued during that month] and [some principal], say M=I+P, and B is your total loan balance. That I is fixed at the amount of interest that accrued that month - you always must pay off the accrued interest. It changes each month as some of the principal is reduced; if you have a 3% daily interest rate, you owe (0.03*B*31) approximately (plus a bit as the interest on the interest accrues) each month (or *30 or *28). Since B is going down constantly as principal is paid off, I is also going down.
The P is most commonly calculated based on an amortization table, such that you have a fixed payment amount each month and pay the loan off after a certain period of time. That's why P changes each month - because it's easier for people to have a constant monthly payment M, than to have a fixed P and variable I for a variable M.
As such, it's important to show you the I amount, both so you can verify that the loan is being correctly charged/paid, and for your tax purposes.
