4-5 point 4-3 approach inside contact, follow-ups
Assuming White took sente at the end of this joseki, Black gets a chance to attack White.
According to the position as a whole, Black may wish to attack directly at the circle-marked point (a vital point of the diagonal of the stones); or to build influence with the cover at the square-marked point (discussed at order of play - temptation).
Suppose Black applies the direct approach . Then the pros usually come out at a. The play at b is a tesuji to help White gain immediate life.
After here, the inducing move at is taught as tesuji. It is possible for White simply to play at c'.
This is from a game Hashimoto Utaro-Suzuki Kensho (B), 1950-01-12. If here, it makes no sense to go back later to the circled point to play hane, after Black has filled in a liberty. So we get . Now it can become ko.
There was no actual ko: White sacrificed the stones and in return weakened , as a big exchange happened.
Simply playing here gives White a high position, that is quite thick from fighting perspective. Later White can hope for White a, Black b as forcing.