Reincarnation

"What we call life...is the combination of the Five Aggregates, a combination of physical and mental energies. These are constantly changing; they do not remain the same for two consecutive moments. Every moment they are born and they die. 'When the Aggregates arise, decay and die, O bhikkhu, every moment you are born, decay, and die.' This, even dow during this life time, every moment we are born and die, but we continue." ― Walpola Rahula, What the Buddha Taught: Revised and Expanded Edition with Texts from Suttas and Dhammapada

The effects of karma reach across lifetimes, karma brings about rebirth.

"Upon those who step into the same rivers, different and again different waters flow." —Heraclitus

It is not some immortal soul that is reborn after biological death. It is a sense of self and an identity that is reborn to form one lifetime.