What's he saying?
"Thy glass will show thee how thy beauties wear, / Thy dial how thy precious minutes waste;"
Your mirror will show you how you age, while your clock shows you how time passes you by;
"The vacant leaves thy mind's imprint will bear, / And of this book, this learning mayst thou taste."
And you will use the blank pages of this notebook to record your thoughts.
"The wrinkles which thy glass will truly show / Of mouthed graves will give thee memory;"
The wrinkles you'll see on your face will remind you of gaping graves;
"Thou by thy dial's shady stealth mayst know / Time's thievish progress to eternity."
You can tell the imperceptible movement of time by looking at your clock or sundial.
"Look what thy memory cannot contain, / Commit to these waste blanks, and thou shalt find"
Whatever you can't remember, write down in this book, and you will discover
"Those children nursed, deliver'd from thy brain, / To take a new acquaintance of thy mind."
That the thoughts you record now will mean more to you when you read them later.
"These offices, so oft as thou wilt look, / Shall profit thee and much enrich thy book."
Writing down your observations will be good for you.
Why is he saying it?
Sonnet 77 continues the theme of the demise of love, youth, and beauty, either of the poet, the fair lord, or both. This theme is addressed in a sequence of sonnets: 49, 63, here in 77, 81, 126, and 154. All these "climacteric" sonnets have numbers that are multiples of 7 or 9, so there is evidence that they were placed purposefully. However, the tone of Sonnet 77 is not as dramatic as the others, since rather than focusing on how horrible it will be when youth is lost, it is hopeful. In recording one's youthful thoughts, one can relive them in old-age by reading the book.
The "vacant leaves" of line 3 are the blank pages of the book around which this sonnet revolves; presumably, the blank notebook has accompanied the sonnet as a gift. Perhaps the mirror and the sundial or clock have also been gifted with the sonnet. The "waste blanks" of line 10 also refer to the blank pages of the notebook, to which the fair lord is urged to "commit" whatever he cannot remember. The idea of being able to "enrich thy book" by recording observations in it is central to this sonnet.
The idea of Time as a thief is common in other sonnets that deal with the theme of the passage of time. For example, in Sonnet 66, the speaker discusses how Time is "Stealing away the treasure of his spring." Here, in lines 7-8, the poet tells the fair lord, "Thou by thy dial's shady stealth mayst know / Time's thievish progress to eternity." The "dial" could either be a sun dial, in which case "shady" refers to the literal shade cast by the dial to tell the hour of day. It could also refer to the hands of a clock, casting shade on the clock's face.
The "glass," or mirror, is used by Shakespeare in many sonnets to be an indicator of truth. No matter what someone imagines themselves to be, if they look in the mirror, there is no denying what it reveals to them. For instance, in Sonnet 62, the poet bemoans that, "my glass shows me myself indeed, / Beated and chopp'd with tann'd antiquity." His old age is revealed in the mirror, to his distress. Sonnet 103 declares, "And more, much more, than in my verse can sit / Your own glass shows you when you look in it." No matter how he describes the fair lord in his poems, the mirror does better justice to what the young man actually looks like.
Line 11, "Those children nursed, deliver'd from thy brain," compares the thoughts of the fair lord recorded in the book to his progeny. This idea hearkens back to the "procreation" sonnets, in which the poet urges the fair lord to have children so that his youth might survive his own death. In this case, the thoughts are like children, "nursed," or looked after, by the book in which they are left; this is another method of immortalizing his youth.