An influx is a large number of people, or a large amount of money or goods, arriving in one place, especially all of a sudden. You might hear of an influx of tourists in July, an influx of workers into a city, or an influx of cash into a company. The picture is of something flowing in, like water through a gate. It is a news and report word — a little formal. Though actually, influx by itself does not say whether the arrival is welcome. An influx of cheap imports may worry factories; an influx of aid money may be good news. The rest of the sentence carries the feeling. People do not usually use it for one or two arrivals; the point is scale and suddenness.