Design and Appearance Edit
The room, like the other rooms within the hotel, carry a vintage look. The room are small, square-shaped, one-room complexes that, from the inside, appears to have an extra room inside, presumably to be the restroom.
However, this room, unlike the others, has a chair and a long table for members of the Resistance to place their computers on whenever they require space to research their targets and bluepills. The room, with it's vintage style, is also quite clean and less dusty because resistance members travel within the room regularly for business. The room is also used for reaching an exit, where redpills can safely exit from the matrix without any equvications and bluepills, agents, and others from seeing them.
With this understand we have ther right The number "303" appears to be an allusion to the character Trinity, whose name in Christian theology defines the three entities that form a single God: Father, Son, and Holy Spirit. This allusion is supported by Trinity's kiss to the lifeless Neo, whose life functions return as Neo transfigures into The One after exiting the room.
It is also interpreted as Trinity's holy entity is within the room. The Matrix begins with Trinity within the room and ends with The One exiting the room and resurrecting from the dead. The parallel between the character of Trinity and Christianity's Holy Trinity, emerges from the room as those who enter the room receives spiritual power and guidance. Neo resurrects from the dead, Trinity receives help from Morpheus via phone to find an exit and escape safely into the Real World.
303 can also reference to "Roland TB-303" a bass synthesizer, which is often used in electronic dance music genre. The track "Mind fields" by "The Prodigy" on the Matrix soundtrack album, has used Roland TB-303.