The arrangement of modern Christian gatherings is the result of the development of early church architecture.
In the early days, up to the fourth century, Christians worshipped along with Jews in synagogues and private houses. After Jewish and Christian worship separated, Christians continued to worship in people's houses (known as house churches), often the homes of the wealthier members of the community in a particular town.
In the smaller gatherings, the evidence (for example the testimony of the apologist Justin Martyr) suggests that everyone participated in the act of worship. This changed as the church became increasingly "clericalised". Clerics carried out the act of worship at the alter, the congregation observed from a distance.
This gave rise to the "two-room" church, with the mass being celebrated in the Sanctuary and the congregation in the Nave observing through the arched "doorway" between the rooms. In the medieval period, the doorway was partially blocked by a wooden "rood screen" with holes to allow the congregation to observe.
The congregation was arranged in rows. Initially, people seem to have stood to observe the ceremonies before backless stone benches were introduced for the congregation (from about the 13th century in England. Some on the continent were earlier). These were often subsequently replaced with wooden pews. Wealthier members were often seated in private "family pews" (which they paid for).
Rood screens went out of fashion with the Reformation, but the basic layout - with the clerics at the front being observed by the congregation in rows - remained. Aisles allowed processions to run the length of the church and also easier access to the seating. As an architectural feature in churches, aisles were inherited (together with much else) from the design of the Roman basilica (e.g. Trajan's Basilica in Rome).
The issue of "clericalisation" of Christian worship actually remains a subject for debate. Some reformers are still calling for wholesale changes to the current "medieval" form of Christian worship characterised by the layout you described.