What is meant by the half life of a radioactive nuclide?
The time in which 50% of the radioactive atoms has decayed.
The half life of radioactive nuclides is defined as the time in which half of the original number of radioactive atoms has decayed.
Imagine you start with 100 atoms of nuclide X.
X decays to nuclide Y with a half life of 10 days.
After 10 days 50 atoms of X are left, the other 50 have decayed to Y. After 20 days (2 half lifes) only 25 atoms of X are left etc.
For the equation, check this answer on Socratic.