What is the meaning of sealing according to Mormon teaching?

1.

According to the Mormon faith a couple with their children and deceased ancestors can be sealed for time and all eternity in the kingdom of their God providing they remain worthy and keep all of the covenants that they have made. This is why they are seeking out their kindred dead as far back as they can, so that there is an unbroken line back to Adam.

The millennium will be a time to finalise this work when all of the spirit children of Heavenly father will have taken upon themselves bodies hereupon the earth. It will be a time when all of the records of every person that has ever lived will be found and the final great sealing of humanity will take place.

in a short way to say it you get to stay with your family forever, here on Earth and in the after life

2.

The term "sealing" also has a more general meaning, but even that is most often related to an ordinance carried out by the Priesthood.

The sealing within an ordinance occurs when the ordinance requires that a second witness takes part in the act of the ordinance itself. For instance, when the sick are administered to, the first part of the ordinance takes the form of an anointing upon the sick person, then the 2nd Priesthood member, lays his hands upon the sick person's head, and "seals" the work done by the first. In point of fact, this is really what is done in a temple sealing anyway; because the couple to be sealed for eternity have already been previously married ... so the temple 'sealing' acts as the verification and second witness before God that the couple really did intend to be married, and have come before the Lord to seal the previous man-made ceremony and intent before God. It acts as a marriage ceremony repeated, but it now carries authroity that they may be married forever, beyond this life.

We also use the term, "sealed", in relation to a "man's or prophet's 'sealing' of his own testimony with his blood" - in that he seals as a 2nd witness of his life's living standards - those things that he believed in, with his blood - so that he may not only have lived for what he believed in, but has died for what he believed in as well. We call that 'sealing his testimony with his own blood'.

A sealing acts as a Confirmation of the first act.