What figure of speech has been used in line 13 and 14 and why?

The last two lines of "Sonnet 14" are an example of what's called a metaphor. This is a figure of speech which is applied to an object or action to which it is not literally applicable. In lines 11–12 of the sonnet, the speaker urges his lover, the "fair youth," to turn to the matter of procreation, or having children:

As truth and beauty shall together thrive,If from thyself to store thou wouldst convert;

The speaker sees great beauty in the eyes of his lover. And he believes that by having a child, his lover will be able to preserve that beauty, handing it down to the next generation. However, if the speaker's lover does not do this, then the speaker makes the following sad "prognostication," or prediction:

Or else of thee this I prognosticate: Thy end is truth's and beauty's doom and date.

What he means by this is that, if his lover does not have children, then the great beauty he has within him, and the truth it represents—for truth and beauty were thought to be synonymous in Shakespeare's day—will die with him. The speaker's reference to a prediction in the last two lines of the sonnet relates to the earlier part of the poem, where he claimed that he read the future not by examining the stars but by gazing into the eyes of his beloved. And those beautiful eyes of his tell him so much more about the future than astrology ever will.
http://www.shakespeare-online.com/sonnets/14.html