Answer: They were arrested for breaking into the Democratic National Committee (DNC) headquarters in attempts to spy on the DNC.
Full background/detail:
The first break-in by burglars associated with the Committee to Re-Elect the President (Nixon) was in May, 1972. The "Plumbers" group (as they were known), broke into the Democratic National Committee office in the Watergate complex of buildings in Washington, DC. They were planting wire-taps on the Democrats' phone lines, and also stole copies of documents. When the wire-taps didn't work properly, they broke in again (in June) to try to fix the surveillance devices, but they were caught.
The formation of the "Plumbers" actually preceded Watergate. They were a "special investigations" unit that the Nixon White House had set up in 1971 to stop the leaking of classified information. Members of this group were those then later involved in the Watergate break-in (among other activities).
Nixon's role in Watergate was especially in his efforts and those of members of his staff to cover up what had happened. Ultimately, the Watergate affair brought down the Nixon presidency. He resigned in order to avoid impeachment. And the whole affair made Americans more distrusting of government.
