Mothwing Cloak (aka Dash) is the second required ability that you get in Hollow Knight. This ability will make you stay in the air a bit longer and reach places that you are not normally able to with just a normal jump.
Note: the first required ability is Vengeful Spirit and that is needed to be able to find Dash.
How to Find Mothwing Cloak to Obtain Dash
Starting from Dirtmouth, drop into the well and head to the left:

In the next room, hug the left wall and drop down until you see a path that has some green bushes and a lamp.

This next room is blocked by an enemy called Elder Baldur. This Is the same enemy that had to be taken out after receiving the Vengeful Spirit spell. Once you have the vengeful spirit you can then press on and make your way towards the Mothwing Cloak
The next room marks the beginning of Green Path. This new area will not show up on your map until you have found Cornifer the map maker. Luckily, he is not too far away from the start of this area. For the first couple of rooms you will only be able to go to the left. Be sure to stop at the bench in the at the top of the large oval shaped room.
Keep going to the left and you will see a new character, Hornet is just out of reach. The only way to continue is down and to the right. If you keep going you will eventually see papers on the ground and a familiar humming from Cornifer who will see you the map.
Next, from Cornifer you will head back out (left) before dropping down into a new room and to the left.
Here you are VERY close to a bench and it is very worthwhile to get a quick save in. To get to the bench, drop down and take a very quick right to reach a bench. Then go right back to where you were.
The next part will have some simple platforming as you make your way all the way to the left. Eventually you will see Hornet again. Here you can start to climb.
After a short bit your way will become blocked and you will need to pay 50 geo to unlock the door and another bench on the other side of the door
Good thing too because as you keep climbing you will find a path that least to the right and an enemy called the Moss Knight. This enemy is tougher than most of the smaller enemies fought thus far because he has a shield and can be tough to time just right. You are required to defeat the Moss Knight to unlock the door and press on.

Once through the door the only way to go will be up and then to the left. In this rocky region you are close to a new area that you will likely not go back to again for quite some time. As you keep going to the left you will find another character that looks similar to you in the jaws of an enemy. It will be up to you to decide if you want to save Zote or not.
From here you can drop down into the next room. The boss fight is just to the left of this room but do not go straight to the boss fight!
Drop down one more room and take a quick left to find a bench to use as a save point. You will be glad you did.
Hornet is a pretty tough fight especially if you are struggling with the movement of Hollow Knight. She is fast and you are going to have to learn all of her attacks. This boss fight is required in order to get the Mothwing Cloak ability more simply known as dash.
Hollow Knight only has one more ability that you MUST get before things get really interesting. After acquiring the Mantis Claw (aka wall jump) you are able to reach most areas of the game. There are several different paths that you are able to take in order to beat the game. I highly suggest you wonder around to try to find the next ability on your own. If you need help finding the Mantis Claw, Click here for the next guide.