In modern aircraft cabin, close to half of the cabin air is recircualted. As this IATA briefing paper on Cabin air quality - risk of contagious viruses notes:
The cabin air system is designed to operate most efficiently by delivering approximately 50 percent outside air and 50 percent filtered, recirculated air.
The AIVC also notes in Air quality in passenger aircraft:
In early commercial jet aircraft, passenger cabins were ventilated with 100% outside air. In more recent jet aircraft, approximately 50% of the ventilation air is outside air and the remaining 50% is filtered recirculated cabinair.
The reason for using recirculated air is quite simple- fuel savings. From the document Commercial Airliner Environmental Control System- Engineering Aspects of Cabin Air Quality:
At the beginning of the commercial jet airliner age, jet airplanes did not have cabin air recirculation systems,... The primary reason was that early jets were powered by highly inefficient turbojet engines.
As engine technology progressed, turbofans were developed with a core bypass ratio of approximately 2 to 1. Fuel economy improved and the cost of
engine bleed air relative to overall fuel consumption was still sufficiently small to make 100% bleed air to the passenger cabin cost effective.
As modern turbofan engines with high 5 to 1 bypass ratios were developed, fuel consumption to provide engine thrust decreased. However, the fuel consumption relative to extracting bleed air dramatically increased, almost in direct proportion to the higher bypass ratio. For a 767 with P&W 4000 engines, the percent increase in fuel consumption due to bleed air only would be almost four times higher than an equivalently sized turbojet for the same amount of bleed air.
Increase in bleed air fuel consumption with modern jet engines; image from Commercial Airliner Environmental Control System- Engineering Aspects of Cabin Air Quality by Elwood H. Hun et. al.