Besides the large capital outlay of purchasing aircraft an airline has to think about depreciation and resale value of the asset. Post September 11, aircraft prices have gone down sharply and hence aircraft that owned aircraft found their balance sheet in the red as the value of their owned aircraft also depreciated sharply. On the other hand aircraft prices also went down and airlines are capitalising on this and are renewing their fleet at bargain rates. This also means that leasing airplanes has also become cheaper because the lessors are buying the planes for less and there are surplus parked aircraft all over the world which has made supply greater than the demand - hence the lower rates.
An advantage of leasing is that airlines can capacity with demand by changing aircraft more frequently. Another advantage is the fast pace of technology where airlines can compete and offer the latest seat technology (comfort, entertainment etc) as it comes available. This can be done easily by returning the planes to the lessor and obtaining newer ones without the airline having to invest on the equipment itself. This, of course, depends on the leasing agreement.
There is more, much more, to leasing vs purchasing. But I hope you find this useful.