Put in the most simple way, white's classical goal with 1.e4 is to continue 2.d4, occupying the center.
Black plays the Sicilian so that he can, if white continues expanding in the center with d2-d4, exchange his c-pawn for white's d-pawn and gain a 2 vs 1 pawns in the center advantage. In the meantime he doesn't develop his pieces, so there's a disadvantage to that approach, but that's a basic idea of the Sicilian.
White has three fundamental ways to deal with the Sicilian: if he believes black's disadvantage in development is more important than the center pawns, he can go for d2-d4 (usually with Nf3 first), fast development and attack. This leads to exciting games and is the traditional most popular way to deal with the Sicilian.
Two, he can take the Sicilian seriously and still continue with his original idea by playing 2.c3. This 'cancels' 1...c5 because white will just take back on d4 if the pawns are exchanged.
Three, white can decide against d2-d4 for now and look for other ways. Usually this involves putting the pawn on d3 (because leaving it on d2 is awkward). Usually play is slow and both sides' pieces don't immediately touch each other in the opening moves, so a great variety of ways to continue are possible. Your line belongs here.
Combining 2.Nf3 and 3.d3 is a bit odd, in that white has already made some slight concessions -- he can't play with an early f2-f4, and the bishop is locked in -- while black hasn't had to do anything to achieve that. By itself that doesn't mean much, as there are still good ways to continue available, but he's made himself a bit predictable.
Most likely, white will put the bishop on g2 and castle short; this is called the King's Indian Attack, because it mirrors black's setup in the King's Indian Defence.
It's hard to give concrete lines (because so much is possible), but I'd place a pawn on e5 (3...e5 or 3...Nc6 and 4...e5) because it shuts down white's d3-d4 for the foreseeable future, f2-f4 is not possible, and an important plan for white is usually to play e4-e5, but you prevent that. Keep the option of playing your white squared bishop to g4 open.
The so-called 'Botvinnik setup' with pawns c5-d6-e5, Nc6, Ne7, and a bishop on g7 seems like an idea.