What happened between Kirito and Asuna in those 2 years? According to the 2nd episode, Kirito and Asuna met in the first month of SAO. Yet 2 years later, they meet again and it seems they are like complete strangers.

What happened to them in those 2 years? Do the light novels explain this?
During the two years, players teamed up to clear the floors.  However Kirito decided to solo the game (heavily influenced by Sachi's death ep. 3).  This made contact between other players uncommon.  Even though Kirito was a solo player, he participated in Boss Battles.  

Before the boss battles he talked with other players for strategy. Asuna being one of the leaders, and Kirito being one of the strongest of players, would talk to each other or at least be in the same area.

It was referenced during the time of Gleam Eyes (Boss of the 74th Floor) when Klein found Kirito in a party with Asuna.