what are lanthanides and actinides

The two rows of elements at the bottom of the Modern Periodic Table are called the lanthanides or Lanthanoids and actinoids or actinides.

Lanthanides - Ce(Z = 58) to Lu(Z = 71)

Actinides - Th(Z = 90)  to Lr (Z = 103)

They are f block elements that means that the last electron in each element is filled in the f- orbital.

They are characterised by the outer electronic configuration (n-2)f^1-14 (n-1)d^0–1ns². 

These two series of elements are also called the Inner-Transition Elements (f-Block Elements).

They are all metals.