Airports charge the airlines for using the facilities (afterall the airport authorities are the one who has to do the maintenance at the airport, organising the schedule etc) and costs/fees charged from one airport to another is different. Airlines are charged for the use of the airport lounge, they're charged for parking bay, they're charged for taxiing, they're charged for runway time (prime time slot will cost more) etc.
The charges also of course corresponds to the number of airports in the itinerary. Say, you're flying out from LAX to London Heathrow direct - therefore the charges would be total from charges of these two airports. However, if you're flying with a stopover, say in JFK, then the charges would be the total charged by all 3 airports. Larger hubs charge more than smaller airports in general.
Not only that, depending on the category of the flight that you're in (e.g. long haul or medium distance or short haul) there would be a different category of charges involved too.
On top of that, the government would also have levied fees or taxes. A lot of airports implement a levy on increased securities since the incidents of September 11 and liquid threat. There are also a variety of other governmental charges such as charging for "departure tax" (Ireland, from 2009 onwards) and carbon tax on fuel (Sweden, Finland, UK etc).
Everything adds up at the end of the day. In Europe, often low cost, no frill airlines such as Ryanair would even offer free flights (as in NO cost for flights) but once all these taxes and charges are included, final price total does increase significantly (although still cheaper than most operators anyway, therefore remaining a popular travelling option even if many would grumbles about their charges and lack of customer service).
Have a look at this link - Austrian Airlines give some insights on how some airport charges are approportioned : http://www.aua.com/us/eng/Flights/Tips/Tax/beispiel.htm
Some airports charge facility fees, then there are government levied fees. In the US this includes the September 11th Security Fee which is $2.50 per segment flown through US airports.
Most airlines now include fuel surcharges in their 'taxes' portion. Although this is a cost of business it means that:
1) Those using frequent flyer miles still pay the fuel surcharges
2) Large companies may have contracts with the airlines that give them a decent percentage off the cost of the ticket, however, this is only off the base fare cost. By putting the fuel surcharge cost in the 'taxes' portion the airlines get around putting a discount on that too.