What are shown at the bottom of the periodic table in order to keep the table a reasonable size?
The lanthanides are generally found in the top and bottom rows beneath the main body of the periodic table, the actinides are below them.
That's because the lantganides and actinides woukd require 14 additional columns each having only two elements apiece, meaning the table would have a lot of "dead space" above them.
Lanthanides are so called because they come after lanthanum in atomic number (lanthanum = 57, lanthanides = 58-71) and they have properties more or less similar to lanthanum. Actinides, below the lanthanides in the usual version of the periodic table, have a similar relationship with actinium.