On one of my most recent posts, some LDS and non-LDS christians were having a great discussion about what the definition of scripture is for each of us.  I do not claim to be the expert on this topic for either LDS or non-LDS, but I can definitely share my personal thoughts and also point to what others have said that I agree with on this topic.

My first thought when researching this is to turn directly to the LDS Bible Dictionary.  The definition is:

The word scripture means a writing, and is used to denote a writing recognized by the Church as sacred and inspired. It is so applied to the books of the O.T. by the writers of the N.T. (Matt. 22: 29; John 5: 39; 2 Tim. 3: 15). For an account of the process by which the books of the O.T. and N.T. came to be recognized as scripture, see Canon. Latter-day revelation identifies scripture as that which is spoken under the influence of the Holy Ghost (D&C 68: 1-4).
This definition gives us a good start, but it can lead to various interpretations.  According to this, it states that scripture is writing that is recognized by the Church, but also scripture are words spoken under the influence of the Holy Ghost.  Therefore, one could interpret scripture to mean that it is anything shared by inspired men or women prophesying.  This can be confusing for people.  Especially if what one is speaking by the power of the Holy Ghost may not reflect one’s personal convictions.  Or worse yet, may not be validated with other scriptures.
I believe that according to this definition, scripture has two parts, or definitions to it.  The first part is scripture for the Church.  The second is prophecy or divine revelation for individuals. 
Scripture for the Church as a Whole (Canon)
Once again, a great first step is to research the Bible Dictionary under “Canon”.  According to the Bible Dictionary, LDS believe Canon is “used to denote the authoritative collection of the sacred books used by the true believers in Christ”.  The dictionary then goes on to attempt to describe how our current Bible became canon and the test of how to decide if writings should be considered scriptural or not.  The test to see if something is scriptural includes these three questions:
Is it claimed that the document was written by a prophet or an apostle?
Is the content of the writing consistent with known and accepted doctrines of the faith?
Is the document already used and accepted in the Church?
Personally, I like the similar definition given by George Cobabe from FAIR.  In his article on The White Horse Prophecy, he describes how the LDS church deems a writing to be considered scripture for the Church as a whole.  First, it needs to be revealed through the prophet.  Next, it needs to be accepted by the Quorum of the Twelve Apostles.  Finally, it needs to be presented to the members of the Church and accepted.  After all of these steps are met, then a writing is considered to be “scripture”. 
This process shouldn’t be foreign to other non-LDS Christians.  It is similar to the councils held thousands of years ago to determine what should be considered scripture.  The second part of scripture should also be familiar with non-LDS christians.
Scripture as Personal Prophecy
The second definition of scripture for LDS according to the Bible Dictionary is “that which is spoken by the power of the Holy Ghost”, which in my mind is essentially prophecy.  From my experience in the LDS church, one of the main ways one can recieve personal scripture is through a Patriarchal Blessing.  In the LDS church, there are men who are set apart and called as “Patriarchs”.  These men give inspired blessings and through the power of the Holy Ghost, prophecy personal revelation for individuals.   
On rare and special occasions, I’ve also seen people prophecy directly to someone but usually I’ve seen things come to pass through giving blessings.  In either case, by definition, this could be called “scripture” as it is given by the power of the Holy Ghost.
Another way people in the LDS church receive “scripture” is through the prophet and apostles speaking.  Typically what I’ve heard is when they speak in general conference and their talks are published you can consider that scripture.  However, I’ve seen people quick to dismiss some things, especially things that were “prophecied” by former prophets such as Brigham Young or Joseph Smith that may have been published but didn’t go through the aforementioned process of canonization.  Therefore, there is some gray area around what to consider as “scripture” or just “inspired”. 
The two parts of defining scripture should be familiar to both LDS and non-LDS christians.  I’m confident that both parties can agree on how the Church as a whole accepts scripture.  The second part, which is less structured, may not be considered to be “scripture” per se for both parties.  A safe way to measure if we can consider what someone prophesies to be deemed as “scripture” is if it lines up with what has been canonized.