Generally speaking, your first step will be to create lines between the origin and destinations. They can be simple straight lines, follow routes, or be representative curved lines - it all depends on how you want the map to look and the legibility of your mapped data. The next step is to get your passenger counts as attributes of the lines you create. Depending on the format of your data, this might be done with a simple or spatial join. Once that's done, you can symbolize your lines based on those numbers. Options include color classification of your passenger count range and graduated symbols controlling line width based on the count or classification, among others. Again, it depends on what you want the map to look like.
There are also some specialty tools that can create such maps, and numerous step-by-step tutorials if you Google the terms 'arcgis flow map'. ESRI has a couple of good ones, including: