Signal strength is a simple measure of the amplitude of the signal that is received. The closer you are to the access point, the higher this will be.

Link quality measures the number of packet errors that occur. The lower the number of packet errors, the higher this will be.

If you are very close to an access point you will get high signal strength, but you might get low link quality due to a microwave oven or cordless phone in the area causing interference.

Conversely, you might be very far from the AP and get low signal strength, but high link quality due to the absence of any RF interference, multipath, etc.