"There are two kinds of people, those who do the work and those who take the credit. Try to be in the first group; there is less competition there." What does this quote mean?

This quote by Indira Gandhi (the late prime minister of India) points to the way some struggle to promote themselves without foundation at the expense of what we might call the "silent majority," those who labor anonymously in factories and backrooms. The fruits of these quiet workers' labor are exploited for personal aggrandizement by the former category of human being. Gandhi's quote is reminiscent of a quote from a relative of the late Italian fascist dictator Benito Mussolini: "Victory has a thousand fathers and defeat is an orphan." Many individuals in all professions place a higher priority on fame and prominence and recognition than on performing the actual work for which they seek recognition. A good leader will unfailingly recognize the vital contributions of those under him or her, being sure to spread the glory while recognizing, to paraphrase a well-worn observation attributed to ancient Rome, "all glory is fleeting."
What Prime Minister Gandhi was suggesting was the simple observation that more gets accomplished when the question of who receives credit is ignored. Many individuals, however, crave recognition, so there is more competition among such individuals than among those who do not seek credit for positive accomplishments. Few, Gandhi suggested, would compete for the privilege of being the worker-bee rather than the queen.
The phenomenon involved here is common. Work ethics and personal integrity differ across the broad spectrum of humanity. Few will compete with you if your goal is simply to be productive and to accomplish the mission. Conversely, the competition is fierce for recognition. Too many people crave attention and give little consideration to the measures involved in achieving a difficult-to-attain objective. That is the meaning behind Gandhi's quote.