Fixed income (or fixed interest) securities pay interest at a rate that does not change with any external variable; the coupon payments are known in advance. Coupons are almost always all for the same amount and paid at regular intervals.
There are two risks with fixed income securities:
The usual alternative to fixed interest is a floating interest rates, which changes the nature of the interest rate risk. A change in interest rate will change the value of a fixed income security but not the income stream it pays. With a floating rate security the value will change less but the income stream will change.
The sensitivity of a fixed interest security to interest rates is measured by duration or, more accurately, modified duration.