The greek word translated watch has the idea of being vigilant or keeping awake.

A selection of verses showing what Jesus and the apostles said about watching.

Jesus told his followers to be awake and vigilant as they didn't know when he was coming back:

Matthew 24 verses 42 - 43

42 Watch therefore, for you don’t know in what hour your Lord comes. 43 But know this, that if the master of the house had known in what watch of the night the thief was coming, he would have watched, and would not have allowed his house to be broken into. 

Jesus was disappointed that his disciples couldn't stay awake and support him in his struggle before his crucifixion:

Matthew 26 verses 40 - 41

40 He came to the disciples, and found them sleeping, and said to Peter, “What, couldn’t you watch with me for one hour? 41 Watch and pray, that you don’t enter into temptation. The spirit indeed is willing, but the flesh is weak.”

Paul urged the Ehesian elders to watch out for those who would corrupt other believers:

Acts 20 verses 30 - 31

30 Men will arise from amongst your own selves, speaking perverse things, to draw away the disciples after them. 31 Therefore watch, remembering that for a period of three years I didn’t cease to admonish everyone night and day with tears.

Paul told the Corinthian believers to be vigilant in standing for the faith:

1 Corinthians 16 verse 13

13 Watch! Stand firm in the faith! Be courageous! Be strong!

Jesus told the church at Sardis to be vigilent in keeping to what they had heard:

Revelation 3 verses 2 - 3

2  Wake up, and keep the things that remain, which you were about to throw away, for I have found no works of yours perfected before my God. 3  Remember therefore how you have received and heard. Keep it and repent. If therefore you won’t watch, I will come as a thief, and you won’t know what hour I will come upon you.