When someone refers to the "basic tenets of Christianity," they are talking about the core beliefs or fundamental principles of the Christian faith. These are the essential doctrines that Christians generally hold to be true. Though there are many denominations the core is common to all. (other than the heretic sects) Here's a breakdown of what that generally entails:

Belief in One God:
The Deity of Jesus Christ:
The Bible as God's Word:
Salvation through Jesus Christ: