What does it mean that no man knows the day or the hour?
It means that while the Lord's return can be recognized as near through the signs Jesus gave, the exact day and hour of His coming is known only to the Father, not even to the angels or to the Son in His earthly ministry, so believers are called to watch and be ready rather than try to calculate the precise moment.
Jesus taught His disciples that after the tribulation, the sun and moon will be darkened, the stars will fall, and then the sign of the Son of man will appear as He comes in the clouds with power and great glory. He gave the parable of the fig tree so that when His followers see all these things happening, they would know His coming is near, even at the door. Yet right after giving these signs, He plainly stated, But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only. In Mark's account this is stated even more strongly, adding that neither the Son knew that day or hour, but the Father alone.
This means the general nearness of His coming can be discerned through the signs He described, but the exact day and hour cannot be pinpointed by anyone, not the angels, and, as Mark records, not even the Son during that time, but only the Father. This is why Jesus compared His coming to the days of Noah, when people were eating, drinking, marrying, and going about ordinary life, not knowing until the flood suddenly came and took them all away. Because the precise timing is hidden, two people could be doing the very same task, such as two in a field or two women grinding at a mill, and one would be taken while the other is left, showing the sudden and unexpected nature of the event for those who are not watching.
Because no man knows the day or hour, Jesus repeatedly commanded His followers to watch and be ready at all times. He compared Himself to a homeowner who could be robbed if the master of the house did not know when a thief was coming, and He said that in the same way, His followers must always be prepared, for the Son of man comes in an hour when He is not expected. He also gave the picture of a faithful and wise servant who is found doing his master's work when the master returns unexpectedly, showing that readiness, not date-setting, is what the Lord requires of His people. Luke's account adds that His followers should watch and pray always so that they may be accounted worthy to escape the things that are coming and to stand before the Son of man.
So while the signs given by Jesus allow believers to know that His coming is near once they see these things beginning to take place, the specific day and hour remain hidden from every man, and from the angels, known to the Father alone. This hidden timing is meant to produce constant watchfulness and readiness rather than fear or complacency, since the coming of the Son of man will come upon the unprepared as a snare, but should not surprise those who are watching.
The scriptures
Immediately after the tribulation of those days shall the sun be darkened, and the moon shall not give her light, and the stars shall fall from heaven, and the powers of the heavens shall be shaken: And then shall appear the sign of the Son of man in heaven: and then shall all the tribes of the earth mourn, and they shall see the Son of man coming in the clouds of heaven with power and great glory. And he shall send his angels with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other. Now learn a parable of the fig tree; When his branch is yet tender, and putteth forth leaves, ye know that summer is nigh: So likewise ye, when ye shall see all these things, know that it is near, even at the doors. Verily I say unto you, This generation shall not pass, till all these things be fulfilled. Heaven and earth shall pass away, but my words shall not pass away. But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only. But as the days of Noe were, so shall also the coming of the Son of man be. For as in the days that were before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noe entered into the ark, And knew not until the flood came, and took them all away; so shall also the coming of the Son of man be. Then shall two be in the field; the one shall be taken, and the other left. Two women shall be grinding at the mill; the one shall be taken, and the other left.
But in those days, after that tribulation, the sun shall be darkened, and the moon shall not give her light, And the stars of heaven shall fall, and the powers that are in heaven shall be shaken. And then shall they see the Son of man coming in the clouds with great power and glory. And then shall he send his angels, and shall gather together his elect from the four winds, from the uttermost part of the earth to the uttermost part of heaven. Now learn a parable of the fig tree; When her branch is yet tender, and putteth forth leaves, ye know that summer is near: So ye in like manner, when ye shall see these things come to pass, know that it is nigh, even at the doors. Verily I say unto you, that this generation shall not pass, till all these things be done. Heaven and earth shall pass away: but my words shall not pass away. But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father. Take ye heed, watch and pray: for ye know not when the time is. For the Son of man is as a man taking a far journey, who left his house, and gave authority to his servants, and to every man his work, and commanded the porter to watch. Watch ye therefore: for ye know not when the master of the house cometh, at even, or at midnight, or at the cockcrowing, or in the morning: Lest coming suddenly he find you sleeping. And what I say unto you I say unto all, Watch.
And there shall be signs in the sun, and in the moon, and in the stars; and upon the earth distress of nations, with perplexity; the sea and the waves roaring; Men’s hearts failing them for fear, and for looking after those things which are coming on the earth: for the powers of heaven shall be shaken. And then shall they see the Son of man coming in a cloud with power and great glory. And when these things begin to come to pass, then look up, and lift up your heads; for your redemption draweth nigh. And he spake to them a parable; Behold the fig tree, and all the trees; When they now shoot forth, ye see and know of your own selves that summer is now nigh at hand. So likewise ye, when ye see these things come to pass, know ye that the kingdom of God is nigh at hand. Verily I say unto you, This generation shall not pass away, till all be fulfilled. Heaven and earth shall pass away: but my words shall not pass away. And take heed to yourselves, lest at any time your hearts be overcharged with surfeiting, and drunkenness, and cares of this life, and so that day come upon you unawares. For as a snare shall it come on all them that dwell on the face of the whole earth. Watch ye therefore, and pray always, that ye may be accounted worthy to escape all these things that shall come to pass, and to stand before the Son of man.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.