The primary objective of the American airborne landing is Normandy were threefold;

• To assist in a quicker movement off the beaches.

• To lessen as much as possible the amount of enemy forces that could be immediately brought to bear against the beachhead by controlling routes of approach.

• Using 1. to expedite the capture of proper port facilities (i.e., Cherbourg) before the enemy could damage them sufficiently enough as to be unusable for an extended period of time.

Utah Beach was on the neck of the Cotentin peninsula and geographically separated from the other four landing beaches by the Douve River estuary; the river itself and an area of swampy land surrounding it. The Germans had blown up flood control devices which waterlogged the low-lying farm fields behind the beach, and planted stout stakes to deter any airborne operations (theoretically, drowning parachutists or tearing the wings off of gliders). The only routes into the interior of the Cotentin peninsula free of any such obstructions were across causeways coming off the beach, or over the roads going through the town of Carentan; the Germans holding either could delay or even stop the Utah force. Capturing the area around the Merderet River and the town of Sainte Mère Église would create a defensive line and stop any threat to the entire length of the Utah beachhead directly from the west.

Map of intended drop zones.

Paraphrased from Warren;

82nd Airborne Division (Mission Boston):

82nd Airborne Drop Zone "N": (west of the Merderet River)

• Seize the crossings over the Merderet River at La Fière and Chef-du-Pont, destroy the highway bridge over the Douve River at Pont l'Abbé, and block all approaches from the west.

82nd Airborne Drop Zone "O": (east of the Merderet River)

• Capture the town of Sainte Mère Église.

82nd Airborne Drop Zone "T" (west of the Merderet River)

• Seize the crossings over the Merderet River at La Fière and Chef-du-Pont, destroy the highway bridge over the Douve River at Pont l'Abbé, and block all approaches from the west.

101st Airborne Division (Mission Albany):

101st Airborne Drop Zone "A":

• Seize the exits of Causeways 3 and 4 (northern), eliminate Germans near St. Martin de Varreville, and establish a defense on the north flank of the 101st Airborne Division on a line running from St. Germain-de-Varreville to the 82nd Airborne Division near Beuzeville-au-Plain.

101st Airborne Drop Zone "C":

• Seize Causeways 1 and 2 (southern) and clear the Germans from the vicinity.

101st Airborne Division Drop Zone "D":

• Seal off of the southern flank of the Utah beachhead.

The glider missions flown on D-Day (Detroit for the 82nd Airborne Division and Chicago for the 101st Airborne Division) were used in a support fashion, landing heavier equipment, ammunition, and much-needed sustenance and medical supplies too awkward to drop via parachute.

Source:

Warren, John C. USAF Historical Studies No. 97: Airborne Operations in World War II, European Theater. Montgomery: United States Air Force Historical Division Research Studies Institute, Air University, 1956.

u/the_howling_cow has given an excellent overview of the American side of the battle, so I'll speak to Operation Tonga and Operation Mallard, the landings of the British 6th Airborne Division on June 6th.

https://imgur.com/a/yq5CUh9 - The 6th Airborne Division's parachute Drop Zones (DZs), glider Landing Zones (LZs), and the objectives for Operation Tonga and Operation Mallard. Note: Sword Beach is just west of Ouistreham.

The 6th Airborne Division had four main objectives on D-Day. Allied planners realized that seaborne troops could not reach these objectives quickly enough, hence the need for airborne landings. Unlike the American sector, the area was less marshy. Bridges, not causeways were the crucial thing here.

1. Capture and defend two bridges: one over the Caen Canal and one over the Orne River. British troops advancing off Sword Beach needed these bridges to expand and secure the eastern flank of the beachhead. This task fell to gliderborne Company D, 2nd Battalion of the Oxford and Buckinghamshire Light Infantry ("Ox and Bucks"). Lord Lovat and his Commandos from 1st Special Service Brigade would land ashore on D-Day and rush ashore to relief them. 7th Parachute Battalion from 5th Parachute Brigade would secure Benouville to help protect the bridges from the West. The 12th and 13th Parachute Battalions of 5th Parachute Brigade would take Ranville, which would protect the bridges from the more vulnerable eastern side.

2. Destroy five bridges to the east: two bridges over the River Divette and the three bridges over the River Dives. This would prevent Germans from moving in reinforcements to hit the beachhead from the east. 1st Canadian Parachute Battalion from 3rd Parachute Brigade would escort engineers to blow the Divette Bridges. Its sister unit, 8th Parachute Battalion would do the same to the Dives bridges.

3. Destroy the Merville Gun Battery. The battery had four war trophy Czech 100mm guns in concrete casemates that could fire on troops landing on Sword Beach. Aerial bombardment in May had failed to destroy the battery, so an assault by airborne troops was needed to take it out. This task was given to 9th Parachute Battalion, part of 3rd Parachute Brigade.

4. Secure the left flank of the landings. By holding positions SE of the invasion beaches, they could hamper German counterattack and help clear out German resistance, making it easier for the troops coming ashore to break out. After blowing its bridges, 3rd Parachute Brigade would hold a large ridge (light green on the map) north of Sanerville.

The British and Canadian paratroopers of the 6th Airborne Divisions would be carried by the glider-towing Stirlings and Halifax's of the RAF's 38 (Airborne Force) Group and the Dakotas of 46 (Transport) Group would drop the paratroopers.

Because there were not enough aircraft, the 6th Airborne had to be delivered in two major lifts: Operation Tonga and Operation Mallard. Contrast this with the Americans, who had enough C-47s and C-53s to drop almost two entire airborne divisions in one go.

1. Operation Deadstick: At 0115, Major John Howard's D Company of the 2nd Battalion, "Ox and Bucks" lands in 6 gliders on LZ X and LZ Y. They plan to stage a coup de main to seize the Orne and Caen Canal bridges before the Germans can blow them up.

2. Operation Tonga: Phase I of Tonga begins at 0120, when 60 pathfinders from 22nd Independent Parachute Company mark DZ N, DZ K, and DZ V with Eureka radio homing beacons. Advance parties from 3rd and 5th Parachute Brigades also land to secure and prepare the DZs. In Phase II, at 0150, 3rd Parachute Brigade drops on DZ K and DZ V, while 5th Parachute Brigade jumps over DZ N. A few Horsa gliders land as well. Six land on LZ V, carrying equipment for the Merville Battery assault. Six more land on LZ K. The engineers of the 591st Parachute Squadron land and spend the next few hours frantically blowing up "Rommel's Asparagus" obstacles to clear two landing strips for gliders. During Phase III at 0420, divisional headquarters and support equipment arrive in 72 gliders.

3. Operation Mallard: On the evening of D-Day at around 21:00 gliders bring in the 6th Airlanding Brigade, the twenty Tetrach light tanks of the 6th Airborne Armoured Reconnaissance Regiment, and an artillery battery from the 53rd Light Regiment. Most of their gliders land on LZ N at Ranville, but some also land at LZ W.

4. Amphibious landings. On D+1, June 7th, the remainder of 6th Airborne was landed by sea. There just weren't enough transports or gliders to land them by air! Note: The 101st Airborne's 327th Glider Infantry Regiment had a similar fate and were landed on Utah Beach due to aircraft shortages.