Before getting to the answer of this question, it is first necessary for us to understand the time period and the circumstances people in the United States faced. In 1932, the US was in the middle of a major economic downturn called the "Great Depression." During the Great Depression, many Americans found themselves out of work, and jobs were not exactly easy to come by. The Bonus Army was made up of World War I veterans and their supporters, many of whom found that they were not immune to the difficult economic situation facing the nation. With many of these war veterans out of work, they sought to receive full cash payment for service certificates they had received for their service. The certificates were to serve as a bonus for wages that were lost by the veterans during their time in the military (because they could not work their regular jobs at home). The problem with this was that the payment for these certificates was not supposed to occur until 1945. As you can imagine, many of the World War I veterans making up the bonus army were hopeful that they would receive payment more immediately in order to alleviate the financial stress they were under.
So, you may ask, why didn't the US government simply give out the payment sooner and avoid conflict with the veterans? There were some members of the US government who supported the veterans' demands. Wright Patman, a congressman from Texas, even attempted to pass legislation which would allow for immediate payment of the veterans. This legislation was opposed by President Herbert Hoover and Republican congressmen. The argument opposing the immediate payment was that the payment would have to come as the result of increased taxes. Increasing taxes during the Great Depression, a time in which many Americans were already struggling financially, would not be a popular decision and could lead to the slowing of potential economic improvement. Ultimately the legislation was not passed at this time.
In order to explain why one would join the Bonus Army and march on Washington, D.C., you simply need to consider the times and the situation faced by the World War I veterans in the early 1930s during the Great Depression. You can definitely see why joining the Bonus Army would have been an appealing option.
The response of the US government to the Bonus Army was not a warm one. Police and, eventually, the US Army (led by General Douglas MacArthur) were dispatched to remove the Bonus Army. This situation eventually led to conflict between the groups and the deaths of two of the demonstrators. Police used bayonets and tear gas, and the army even brought tanks to disperse the demonstrators. You can certainly imagine how a member of the Bonus Army would feel and react in this instance.
The fighting between police, with the support of the US Army, and the demonstrators was shocking. Although the goal of the veterans was not initially achieved, the government did realize that there was a big problem that needed to be dealt with. In response, the US government created the Civilian Conservation Corps in 1933, which helped to employ many unemployed veterans. Three years later in 1936, the US Congress passed a bill, and overrode a presidential veto, to allow the veterans to redeem their certificates early and receive payment. The bonus march helped to establish the need of the US to ensure that their returning war veterans were taken care of and properly compensated after serving their country.