The "nearest second" refers to the nearest whole second, rounded up or down.
If your exact position is 42° 21 ' 30.4 ", the position to the nearest whole second would be 42° 21 ' 30 ". The number could be rounded up or down depending on the fraction.
Longitude involves and imaginary circle running East-West, divided into 360 degrees. Each degree is divided into 60 minutes (denoted with '). Each minute of angle is further divided into 60 seconds (denoted with ").
At the level of Boston, each second is about 60 meters (somebody can correct me if they like)
Look in google for "navigation longitude latitude) and you should find an explanation