What exactly is this tawheed that is so important, that which holds such a high position?

Linguistically, the word tawheed comes from the word wah-hada, which means to make something waahid (singular). Waahid is the opposite of two, three, etc., the opposite of plurality. So waahid is something that will continue to be singular and never become a partner of something else. As for the sharee'ah (shari'ah)'s definition, the tawheed means to single out Allah with all forms of worship, so that you make all of your worship for Allah alone.

Allah says: "...and the religion will be entirely for Allah"¹. The word religion in this verse means worship, as Allah says: "and I have not created the Jinn nor Mankind except to worship Me"². And Allah says: "and worship Allah, and do not ascribe a single partner to Him"³. Allah also says: "So call on Allah, making the religion entirely for Him, even if the disbelievers detest it"⁴.

This is the meaning of tawheed - to single out Allah in all acts of worship and to abandon the worship of anything else.

Source: Meaning of the word Tawheed

Footnotes:

[1] the meaning of Soorah Al-Anfaal (8):39

[2] the meaning of Soorah Ath-Thaariyaat (51):56

[3] the meaning of Soorah An-Nisaa' (4):36

[4] the meaning of Soorah Ghaafir (40):14