As is written on page 15 of our free lecture notes:
“Different investors are interested in different segments of the yield curve. Short-term yields, for example, are of interest to financial intermediaries such as banks. Hence the shape of the yield curve in that segment is a reflection of the attitudes of the investors active in that sector. Where two sectors meet there is often a disturbance or apparent discontinuity in the yield curve as shown in the above diagram.”
The ‘kink’ is the disturbance or apparent discontinuity.