Why might it be important to get a Lowe interest rate on a mortgage?

The shortest and simplest answer is because it saves you money.

For example:

(These numbers are over-simplified, they only factor in price, rate, and term. Actual mortgage numbers are more complicated.)

$150,000 house

30 year mortgage

3.5% rate

$673.57 monthly payment

Total Payments ---- $242,485.20

$150,000 house

30 year mortgage

5% rate

$805.23 monthly payment

Total Payments ---- $289,882.80

$150,000 house

30 year mortgage

7% rate

$997.95

Total Payments ---- $359,262.00

As you can see, even small differences in interest rate make a huge impact. At the end of the loan, there's a $47,397.60 difference between a 3.5% and 5% rate, and a $69,379.20 difference between 5% and 7%.

So yes, it's very important to get a low interest rate.