The differences between Simple and Compound Interest are quite easy to understand.

Simple interest is interest which has been calculated on the original value of the loan or investment. It will be quoted as a percentage per annum (ie. per year) eg. 12% pa and the amount of interest received or paid each year will not change unless the loan or investment amount changes.

Compound interest is also usually quoted as a percentage rate per annum but may be levied, or calculated, more than once per year eg. monthly or quarterly. The difference with compound interest in that the amount of interest calculated is added to the initial value of the loan or investment every time it is levied. Over time, the amount of interest will then increase, provided the initial loan or investment amount has not changed.

I'll use an example to illustrate:

Imagine you have invested $1,000 in an account at 7% interest pa for 3 years.

1. If the interest rate is a simple interest rate:
At the end of year 1: Interest = $1,000 x 7% = $70 (value of investment = $1,070)
At the end of year 2: Interest = $1,000 x 7% = $70 (value of investment = $1,140)
At the end of year 3: Interest = $1,000 x 7% = $70 (value of investment = $1,210)

As you can see, the interest amount remains the same every year and the total investment amount just increases by $70 per year.

2. If the interest rate is a compound interest rate:
At the end of year 1: Interest = $1,000 x 7% = $70 (value of investment = $1,070)
At the end of year 2: Interest = $1,070 x 7% = $74.90 (value of investment = $1,144.90)
At the end of year 3: Interest = $1,144.90 x 7% = $80.14 (value of investment = $1,225.04)

With compound interest, the value of the investment increases faster over time as you are in reality earning interest on top of interest. This is great of you are earning the money, but not so great if you are paying off a loan! :)