A refracted wave is a wave whose path has been bent
as a result of traveling out of one medium and into into
a different medium, or through a medium whose properties
change slightly and gradually over a substantial distance.
Example #1:
The light waves that enter your eyes as you look down from a
bridge and watch a fish in the creek below you. The fish is not
where you think it is. The light waves coming from it are refracted
when they travel out of the water and into the air. Your brain doesn't
include that bend in its calculations, and it naturally assumes that the
fish is in the direction the light waves are coming from. But it's actually
in a slightly different direction.
Example #2.
If you wear glasses or contacts, then all the light waves you see
through them are refracted on their way through your 'corrective
lenses' before they enter your eyes.
Example #3.
When you listen to an AM radio station at night that's located in
a city very far away from you, the radio waves you're receiving
are coming at you from a direction in the sky.
Now you KNOW that the radio station is not located there. Some of
the radio waves from the station leave the transmitting tower at an angle high above the ground, and head off into the sky. As they travel far through the air ... sometimes hundreds or even thousands of miles ... the properties of the air change gradually, and the radio waves are gradually refracted as they travel, eventually curving downward toward the ground again.
(I'm writing this answer while I'm on a buisness trip to a city that's
about 650 miles from home. Two nights ago, while I was in the car,
I got a little bit curious, and I tuned the car radio to a popular AM radio
station back in my home town, just to see.
And there it was ! Booming in. 5 by 9 with practically no Q R Mary.)