An iambic keyer is used with two paddles. The concept is that you can hold down one paddle, say the dah paddle, to send out a string of dahs. While doing this, if you tap the dit paddle, it will insert a dit between the dahs.
If you hold both paddles at the same time, the iambic keyer will send alternate dits and dahs. The difference between mode A and mode B iambic keying is what happens when you release both paddles. In mode A, the keyer will finish with the last dit or dah that it was sending at the time of release. In mode B, if it was sending a dah when you release the paddles, it will add one more dit. If it was sending a dit, it will add one more dah.
It is widely held (no pun intended) that mode B came about because of a logic error on an early iambic keyer. Operators got used to the effect and then found it difficult to use a corrected (mode A) keyer. As a result, most keyers offer the option to switch between mode A and mode B.
The first keyer I used was a Heathkit unit that was mode A. When I try a mode B keyer, I am often making sending errors. There is no right or wrong mode - both are well established. The receiving station cannot tell the difference. It is down to a matter of operator training and preference.