What does ROUTE mean on an oversize permit?

Route. A numbered route. Whether it's a state, US or Interstate route depends on the state: Connecticut and Hawaii write state routes as Route 15 or Route 93.

Also printed as RT, RTE.

On real permits

PrintedMeansState
Route 15State Route 15, which is the Merritt Parkway and the Wilbur Cross Parkway. Trucks and oversize loads are not allowed on them.Connecticut
U.S. Route 1U.S. Route 1 (Boston Post Road)Connecticut
Route 93Farrington Highway on Oahu, from the H-1 Palailai Interchange to the Kaena Point State Park boundaryHawaii
Route 92Ala Moana Boulevard in HonoluluHawaii
U.S. Route 1U.S. Highway 1, also written Route 1 in Maine rulesMaine
State Route 159Nevada State Route 159. Its mileposts 0.0 to 14.0 are closed to trucks over 26,000 pounds declared gross weight unless the trip starts or ends there.Nevada
[HISTORIC ROUTE 66]Another name for the same road, shown in square brackets. It is not a separate road to take.New Mexico
TR 209 (Traffic Route 209)Signed route 209. PennDOT's permit conditions write signed routes as 'Traffic Route' or 'TR'.Pennsylvania
Route 95Interstate 95. RIDOT's restriction list writes interstates as 'Route' plus the number, like 'Route 95 South CD Road'.Rhode Island
Route 195Interstate 195, the road over the Washington Bridge in Providence.Rhode Island

Decode a whole route line