Because the previous educator did such a great job in describing Garvey's importance in Malcolm X's life, I will merely provide a bit of additional context about Garvey.
Marcus Garvey, a Jamaican immgrant, developed the United Negro Improvement Association (UNIA) in the 1920s in New York City after the First World War. Many black men had returned to the United States as war veterans and faced mistreatment and ingratitude for their service. In some cities, such as St. Louis, riots broke out in 1919 due to fears that black people would seek equality as a result of participation in the war. The spate of riots were nicknamed "Red Summer," a time when many black people were brutally murdered by whites in the street. St. Louis native Josephine Baker, who was thirteen years old at the time, recalled fleeing the city with her family and watching as a pregnant black woman's stomach was cut open by raging white people.
Aside from this horror, the postwar period was also the beginning of the Harlem Renaissance. It was not only a literary movement, but also a pursuit of more expansive ideas about black representation in visual art, African motifs, and community and blackness that progressed beyond the legacy of slavery.
Garvey, in his work, addressed the desires to escape racism and achieve self-actualization. His organization's goal was to transport blacks back to Africa. Through his newspaper, Negro World, and his shipping company, Black Star Line, he developed trade and transportation between black businesses in the Americas and Africa.
In addition to his economic power and international influence, what made Garvey a threat (I think this is more accurate than perceiving him as "controversial") was his combination of Booker T. Washington's message of self-sufficiency with anti-imperialism and his encouragement of organizing black people around an understanding of a shared lineage and resistance to white supremacy.
Whites did not mind Washington's message of self-sufficiency because he discouraged black migration out of the South, which would still allow for the exploitation of black labor. Also, his focus was on black people in the South, whereas Garvey's message was diasporic and threatened to undermine economic interests.
In the end, though, the UNIA was "the largest black secular organization" in black history, Garvey could not succeed in expatriating black people to Africa. He failed to gain the support of black leaders in other organizations, and he underestimated the extent to which colonialism worked against him. FBI chief J. Edgar Hoover exploited these weaknesses to destroy Garvey and the organization. He was arrested for mail fraud and convicted in 1923. He was imprisoned in 1925 and then deported to Jamaica in 1927.
Garvey's ideas about black diaspora survive today. They became especially popular in the late 1950s when the collapse of colonial rule in West Africa made it more feasible for black people, particularly from the United States (e.g., W.E.B. DuBois, Nina Simone, Stokely Carmichael) to expatriate themselves to Africa.