Within Chinese Medicine, the heart is considered to be the most important organ in the body and is often termed as the Emperor. Functionality dictates that the heart pumps blood from both a Chinese and Biomedical perspective however the heart also has several other functions in the TCM framework.
1) Governs Blood: as mentioned above, the heart is responsible for pumping blood throughout the body. It is also responsible for the transformation of Gu–Qi (nutrients taken from food) into blood. This particular concept confuses students as it is said that the Spleen makes blood (with help from the kidneys) and this is true however consider the heart to be the factory foreman that ensures the spleen and kidney know their respective roles.
2) Controls the blood vessels: this refers to the quality of the pulse and how it reflects the condition of the heart. It also reflects the middle level of pulse when considering an overall picture of health (variation in the middle position would mean disease in the heart or liver).
3) Manifests in the complexion: much like the quality of the pulse reflecting the condition of the heart, the facial complexion does the same. A pale face can mean heart blood deficiency and a red face can mean heart heat, it is a varied list and one should also keep in consideration the other organs can be reflected upon the face as well.
4) Houses the Mind: the proper term to use is Shen and it is a very elusive term to try to translate into English. It can be summarised as consciousness or mind however that is still too shallow as the concept of Shen also relates to sleep, memory, thought and every emotion we feel. Discussing emotions in TCM is a very complex issue as there is much intertwining and intricate relationships, books could (and have) been written on the topic and yet there are few that conclusively understand all of it. Just know that damage to the heart can lead to problems with sleep, memory, thought process and emotions as the heart is the Emperor and the Emperor foresees all below him.
5) Related to Joy: The emotion that can damage the heart most is joy. This seems like an odd concept however the Joy mentioned here is more akin to euphoria. Think of it as an overindulgence in joy either through short term fixes (online shopping for example) that lead to an instant release of dopamine that is short lived. Constantly seeking that short term satisfaction can lead to damaging the heart as it is believed too much joy causes the heart to expand (excitement makes the heart beat faster).
There are more features to the heart including the relationship it has with the tongue, sweating, bitter flavours and scorched smell however the information above covers the main points that should be known when exploring the functions of the heart in Chinese Medicine.