Symphonic rock, or classical rock as it is also commonly called, is what happens when electric guitars and symphony orchestras collide. The results are often not pretty — there's a reason nobody remembers that album Deep Purple did with an orchestra, for example. But ever since the Beatles experimented with the idea of adding classical flourishes to Sgt. Pepper, some rock groups have been likewise drawn to the symphonic rock idea like moths to a flame.
The most successful symphonic rock band was arguably the Moody Blues, although other bands like Procol Harum, Renaissance, and Emerson Lake & Palmer have also found varying degrees of success melding guitars and drums with violins, oboes, and cellos.
A significant number of bands like Yes, Genesis, and the Moodies (those guys again) have also used string synthesizers — and an instrument called the mellotron, in particular — to achieve the same effect. These records generally fall under another rock sub-genre called prog or progressive rock.
You'll find bloggers talking about symphonic rock at sites like Prog Archives.