Quadriga was the term used to describe the four major latin authors whose work formed the basis of a classical education for many hundreds of years. The choice of authors reflected the purpose of a classical education, with attention focussed on oratory and cultural history.
Vergil (Publius Vergilius Maro) was the first member of this "four-horsed chariot", included for the quality of his poetry and for the cultural significance of the Aeneid, with respect to the mythical foundation of Rome and the values to be upheld by every Roman citizen.
A classical education was essentially geared towards producing an orator (see Quintilian, On Oratory); thus Cicero (Marcus Tullius Cicero) was included in the group of four in order to instruct young boys to the necessaries of making speeches.
The playwright Terence (Publius Terentius Afer) assumed his place in the Quadriga for the moral guidance and useful quotes that were afforded by his plays. Again, the moral overtones were important in the instruction of Roman citizens, whilst the quotations were useful when making speeches!
Finally, Sallust (Gaius Salustius Crispus), whose histories presented yet more moralising, and quite a good read, too (if you like that sort of thing).