Lady Capulet utters these words and is often characterized as one of the more vain players on this stage.
What she means with these words as she casts first glance on her dead daughter's corpse is that to see a child of hers already laid to rest in a tomb makes her feel old. Not only that, but also to have lost a child will continue to age her with grey hairs and wrinkles as stress and sorrow always do.
This word sepulcher means to bury. I think she is noting that since she is burying her daughter, her time might not be that far off.
A sepulchre just means a tomb -- a place to bury people. It's not just a little grave like is usually used in modern times. It's more like an old time tomb where you have a room of some sort where the coffins of lots of people from a particular family are kept.
This line is spoken by Juliet's mom, Lady Capulet, when they find Juliet dead in the tomb. What she means is that death reminds her that she is old and will soon be in a sepulchre herself.