Every time my MacBook goes into standby mode and I wake it up,the display takes a few second to power up. Is this a normal behaviour or should it wake up immediately?
For the most part this is normal, unless it's happening even when it's only been asleep for a few minutes. There are actually two different sleep modes, basic standby and hibernate. If it's been asleep for a long time, the computer will power down more than usual (it's already written everything in RAM to the disk), and in order to get out of that mode it has to read from disk back into RAM. This can take a small amount of time.
For more information, see this article (it's pretty old) or
man pmset in Terminal.