There are several opinions on the intended meaning of Shakespeare's sonnet number 116, and though I am not doing a line-for-line explanation, I would like to express my impressions on this lovely sonnet.
Something that comes up clearly in 116 is the allusion to marriage vows, and I believe that Shakespeare was inspired by those wedding vows to pen his thoughts. The idea of love not altering when alteration it finds seems to be a reference to "in sickness and in health, for richer and for poorer" the couple declares during their vows. Certainly, anyone who has been married for a few years knows that change or alteration is not something that may come, but is certain to come in many different ways.
The words with the remover to remove are quite odd to decipher, though I think he is referring to the idea of "forsaking all others" ... that is, anyone a person has known before the marriage vows are taken or who may come afterward. In effect, saying "no person shall remove me from you." And till death—the edge of doom—the wedding promise is made to last for the married couples' whole lives.
I can just imagine Shakespeare attending a wedding and while he is listening to the vows being recited, he considers how lovely and profound the thoughts are. They only lack a certain flow and rhythm to become poetic. As he is on his carriage ride home, the words and thoughts fill his mind, so that by the time he has arrived there, he rushes to his desk and writes one of the most beautiful expressions of love.
However, though I fear I may come across as pretentious, I will say I am not crazy about the ending of Sonnet 116. I wish that the last two lines would have been on as high a level of thoughtfulness and moving in their scope as what precedes them. As it is, he seems to have hurriedly come up with some way to end his sonnet. I understand he wished to make the thoughts conveyed be personal and therefore ends with a reference to himself, but to me those last two lines are like having a Rolls Royce and putting a Chevy insignia on it.
All that aside, it seems only right that those expressions on the everlasting quality of love were written literally hundreds of years ago and yet are still being read with tender feeling today. They convey the emotions of people truly in love, who wish to demonstrate their love by making a solemn promise to each other by uniting in marriage.
My having been happily married to the same person for four decades, I can personally say with a fair bit of authority that this sort of everlasting love cannot be just a feeling, no matter how deeply it is felt. It must also be a guiding principle that makes the couple determined to stay together through tough times—yes, for better or for worse. Not that it is worse to stay with the person, but circumstances in life sometimes become better and sometimes worse, such as sickness as opposed to health. In ever so many ways, love is more than what can be summed up in just one word, and Shakespeare captures its enduring nature in this beautiful poem.
To conclude, I was inspired by his words to write a clumsy imitation of Sonnet 116, as you see here: