In a few words: land disputes between some very powerful people. To describe it further I'm a Delawarian and a recent graduate of the University of Delaware with a degree in history, so I will see what I can do.
The geography of the state is somewhat unique, and as such the history of it is a little complex. For the sake of clarity and my sanity I am going to try to create a timeline to help.
For some context the Duke of York took the Delaware territories from the Dutch without a title or a charter. This makes all this a little more complex later on.
In 1680 William Penn, the founder of Pennsylvania, petitioned Charles II of England for some land north of Maryland. Penn was able to make this petition of Charles II because Penn's father "served the Crown," and "the debts his king owed his father."
(source: http://archives.delaware.gov/eBooks/EastOfTheMasonDixonLine.epub)
Penn wanted to be the sole owner of this territory, but this meant soliciting the necessary opinions of nearby Lord Baltimore who owned the land now known as Maryland to the west, and the Duke of York who owned land around the noticeable arc at the top of the state. Lord Baltimore had concerns over Charles granting Penn too much southern estate, and the Duke had concerns over the arc which I will talk about now.
Fascinatingly, this 12 mile arc at the top of the state was originally supposed to be 20 miles, but Penn was able to reduce it to just 12 and wanted the arc in the first place so his land would reach further towards the water (it does indeed!). Charles II made this grant to Penn on March 4th, 1681. You can read the necessary section as quoted below if you're interested:
" . . . bounded on the East by the Delaware River, from twelve miles distance, Northwarde of New Castle Towne unto the three and fortieth degree of Northern Latitude . . . the said lands to extend Westwards, five degrees in Longitude . . . and the said lands to bee bounded on the North, by the beginning of the three and fortieth degree[2] of Northern Latitude, and on the South, by a circle drawne at twelve miles distance from New Castle Northwards, and Westwards unto the beginning of the fortieth degree of Northern Latitude; and then by a streight line Westwards, to the limit of Longitude menconed . . . "
[italics my emphasis]
At any rate, Charles II wrote to Lord Baltimore about his grant of Penn's charter which necessitated a meeting between Lord Baltimore and some of Penn's agents. Suspicion and animosity between Baltimore and Penn's agents "grew," and disputes over boundaries failed. This arc was one of the major problems, and the disagreement came to such fine hair splitting details over the specific definition of what a degree is with Penn attempting to use both definitions to his benefit.
In 1682, the Duke of York finally buckled and granted Penn the remaining land within the circle of the arc, but Lord Baltimore would hold out for a little while longer. The top of the state is pretty much defined at this point, but what about the bottom?
In 1683, Baltimore and Penn further disputed over the territory. Baltimore wanted the 40th parallel, and Penn wanted to use 60 miles per degree. Penn was willing to concede if Baltimore gave Penn access to the Chesapeake (water), but Baltimore refused so this dispute made its way back to England where James II (former Duke of York, and friend of Penn's) oversaw the dispute. James II stood firm until Penn raised the argument of Lord Baltimore's charter rights being preempted by the Dutch settlement.
All of the formal information is sourced from this one link. If I find more I will add to this post:
http://archives.delaware.gov/eBooks/EastOfTheMasonDixonLine.epub
There is further information on the Penn-Calvert boundary dispute if you want to go digging. Thank you for reading.