what is the eligibility criteria to compete for this cup?
A qualifying tournament is played.
FIFA World Cup
Since the second World Cup in 1934, qualifying tournaments have been held to thin the field for the final tournament. 
how many times has the host nation won the world cup Brazil has won five times. what sports is the cup related to? Football when did this cup begin? 1930 which organization arranges this tournament? FIFA
wiki:7704223
FIFA World Cup [SEP] Qualification
Since the second World Cup in 1934, qualifying tournaments have been held to thin the field for the final tournament. They are held within the six FIFA continental zones (Africa, Asia, North and Central America and Caribbean, South America, Oceania, and Europe), overseen by their respective confederations. For each tournament, FIFA decides the number of places awarded to each of the continental zones beforehand, generally based on the relative strength of the confederations' teams. The qualification process can start as early as almost three years before the final tournament and last over a two-year period. The formats of the qualification tournaments differ between confederations.