The Hatch Act of 1939, officially known as An Act to Prevent Pernicious Political Activities, was the codification of a 1907 Executive Order signed by President Theodore Roosevelt intended to minimize the influence of partisan politics in the the operation of Executive Branch agencies of the federal government. Passage of the Hatch Act was similarly intended to prevent abuse of federal agencies by politicians for partisan purposes. As federal employees are, obviously, on the federal -- read: taxpayer funded -- payroll, the suggestion that U.S. citizens would be victimized by the partisanship that dominates Washington, D.C. and its extended environs was anathema to many in both major political parties in Congress. The Hatch Act prohibited federal employees, as well as some state employees and others whose positions existed at the whim of the federal budget process, from engaging in political activities, including during their free time after work. The constitutionality of the Hatch Act has been challenged numerous times over the decades, as it can be interpreted as infringing on the First Amendment rights of government employees, but the U.S. Supreme Court has largely upheld the law's provisions. That said, federal employee labor unions successfully lobbied for changes to the Hatch Act that were eventually passed in 1993. While the effect of those changes -- known as the Hatch Act Amendments of 1993 -- has been less than the unions had hoped, it did remove some of the restrictions on whether federal employees could engage in partisan political activities in their free time. It is worth noting that Section 7321 of the 1993 law declared the following:

It is the policy of the Congress that employees should be encouraged to exercise fully, freely, and without fear of penalty or reprisal, and to the extent not expressly prohibited by law, their right to participate or to refrain from participating in the political processes of the Nation.

While Congress, in passing these amendments, acknowledged the extent to which the Hatch Act unfairly constrained government employees, the underlying rationale for the 1939 Act remained. Consequently, the revised Hatch Act continues to prohibit political participation on the part of government employees under certain circumstances, such as the prohibition on the employee's using "his official authority or influence for the purpose of interfering with or affecting the result of an election," and "knowingly solicit[ing], accept[ing], or receiv[ing] a political contribution from any person," unless such person is a member of the same federal labor organization and there is no superior-subordinate relationship involved among interested employees. 

In conclusion, the effect of the Hatch Act was to prohibit involvement in political activities by federal employees, which both protected (to a certain degree) the integrity of the government while imposing constitutionally-questionable restrictions on those same employees. It is a delicate balancing act, but many such laws involve similar attempts at bridging incompatible positions.

The significance of the Hatch Act (passed in 1939) is that it helps to maintain the public trust in our executive branch.  It does this by preventing members of the executive branch from participating in partisan politics. 

Before the Hatch Act, it was legal for members of the executive branch to engage in partisan political activities.  This meant, for example, government workers might go around trying to get out the vote for a given candidate.  It also meant that government workers might be hired on the basis of partisan politics.  This was bad for the country because it reduced trust in government.  Our government workers ought to be doing their jobs as well as they can, helping people regardless of their political affiliation.  We should never have to feel, for example, that we might not get a certain government benefit unless we listen to a government worker’s pitch for a given political candidate.  We also do not want government officials who are hired for political reasons, not because they are well-qualified for their job.

The Hatch Act was significant because it removed members of the federal executive branch from partisan politics, thus “cleaning up” government to a degree.