Terry was born the first child of James "Jim" Daniher and Edna Daniher (née Erwin) on 15 August 1957 at West Wyalong Base Hospital. Terry attended St Joseph's Catholic School, Ungarie for his primary education before going to Ungarie Central School until year ten, after which he became a farmer.
It was during his childhood that Terry showed his love for sport, namely Australian rules football, playing in the Northern Riverina Football League (NRFL) on Saturdays while playing rugby league at school carnivals. It was during his time in the NRFL that Terry won several best & fairest awards before playing with Ariah Park-Mirrool in the South West District Football League for the 1975 season. It was during this season that Terry was approached by the South Melbourne Football Club to play for them.
From 1976–1992 Terry played for South Melbourne and Essendon in the VFL/AFL, playing 313 games and playing in the 1983, 1984, 1985 and 1990 Grand Finals, two of which he won. He also made history alongside his brothers when they became the first quartet of brothers to play for the same team in a State of Origin match and in a home-and-away game. It was after the 1992 season that Terry retired.
After his professional career, Terry returned to the Riverina to play for the Wagga Tigers in the Riverina Football League (RFL), becoming Captain-Coach and leading the Tigers to five premierships out of six Grand Finals.
After this he returned to Melbourne to become an Assistant Coach for Essendon, coaching the team that won the 2000 Grand Final. In 2003, Terry became an Assistant Coach for the Collingwood Football Club before becoming an Assistant Coach for the St Kilda Football Club, where he would stay from 2004–2005. Terry got his final coaching job when he became an Assistant Coach for the Carlton Football Club, where he stayed from 2006–2007. After this, Terry begun his own cleaning business, Terry Daniher Cleaning Services.