We are told that Ddominant7 "resolves" Gmajor, that the F# "leads to" the G and the C "leads to" the B. What does that actually mean?

"Leads to" comes from singing or playing in parts. If the harmony is all made up from vertical combinations of single lines, that's the most likely way to realize it (particularly for a vocal ensemble, anything else would be too hard to sing). Hence the idea of "voice leading".

D going to G melodically is the usual "modal dominant" idea. Ultimately it probably comes from the very ancient tradition of pentachordal melodies - the authentic modes retained the idea of stating the extremes of the pentachordal gamut as a marker of finality. The rest of the harmony is built round that.