Saving is used here as a verbal adjective (a participle). It modifies time and tells us more about its nature; namely, that it is characterized by the activity of saving daylight. It is a saving daylight kind of time. Because of this, it would be more accurate to refer to DST as daylight-saving time. Similar examples would be a mind-expanding book or a man-eating tiger. Saving is used in the same way as saving a ball game, rather than as a savings account.
Nevertheless, many people feel the word savings (with an 's') flows more mellifluously off the tongue. Daylight Savings Time is also in common usage, and can be found in dictionaries.
Adding to the confusion is that the phrase Daylight Saving Time is inaccurate, since no daylight is actually saved. Daylight Shifting Time would be better, and Daylight Time Shifting more accurate, but neither are politically desirable.