Here's a word study on Ease:



Websters 1828 Dictionary:

ease

EASE, n. s as z. [L. otium.]

1. Rest; an undisturbed state. Applied to the body, freedom from pain, disturbance, excitement or annoyance. He sits at his ease. He takes his ease.

2. Applied to the mind, a quiet state; tranquillity; freedom from pain, concern, anxiety, solicitude, or any thing that frets or ruffles the mind.

His soul shall dwell at ease. Ps.25.

Wo to them that are at ease in Zion. Amos.6.

3. Rest from labor.

4. Facility; freedom from difficulty or great labor. One man will perform this service with ease. This author writes with ease.

5. Freedom from stiffness, harshness, forced expressions, or unnatural arrangement; as the ease of style.

6. Freedom from constraint or formality; unaffectedness; as ease of behavior.At ease, in an undisturbed state; free from pain or anxiety.

Scriptures: 

Mosiah 21:15

• Book of Mormon

And now the Lord was slow to hear their cry because of their iniquities; nevertheless the Lord did hear their cries, and began to soften the hearts of the Lamanites that they began to ease their burdens; yet the Lord did not see fit to deliver them out of bondage. 

Alma 39:17

• Book of Mormon

And now I will ease your mind somewhat on this subject. Behold, you marvel why these things should be known so long beforehand. Behold, I say unto you, is not a soul at this time as precious unto God as a soul will be at the time of his coming? 

Mosiah 24:15

• Book of Mormon

And now it came to pass that the burdens which were laid upon Alma and his brethren were made light; yea, the Lord did strengthen them that they could bear up their burdens with ease, and they did submit cheerfully and with patience to all the will of the Lord. 

Amos 6:

• Old Testament

AmosChapter 6Woe to them who are at ease in Zion—Israel will be plagued with desolation. 

Quotes:

.

 He that would live in peace and at ease must not speak all he knows or all he sees.
~Benjamin Franklin

Character cannot be developed in ease and quiet. Only through experience of trial and suffering can the soul be strengthened, ambition inspired, and success achieved.
~ Hellen Keller

 Try to be like the turtle - at ease in your own shell.
~Bill Copeland


My personal definition:
I think Ease has two different meanings. One I think means lazy, like you are to much at ease, so much as not to care about others. And the other meaning I think is deep peace. Like a relaxed sense, like it said "They were at ease because He lifted their burdens."
So there's this Ease: lazy, not caring of others and not doing anything, couch potato. 
And there's this Ease: peace, relaxed, burdens lifted, free, content.

I know that we can have both ease, but lets not be the lazy kind, lets be the serving kind, and we will still be at ease if we are serving, because He can ease our burdens. An there is a deep peace and Ease that comes with serving and doing His will. :)