Praise be to Allah.
The importance of honouring ones parents is:
Firstly: it is obedience to Allaah and His Messenger (peace and blessings of Allaah be upon him). Allaah says (interpretation of the meaning):
And We have enjoined on man to be good and dutiful to his parents [al-Ankaboot 29:8]
And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour. And lower unto them the wing of submission and humility through mercy, and say: My Lord! Bestow on them Your Mercy as they did bring me up when I was young [al-Israa 17:23]
In al-Saheehayn it is reported that Ibn Abbaas said: The Messenger of Allaah (peace and blessings of Allaah be upon him) was asked which deed is the best? He said, Faith in Allaah and His Messenger, then honouring ones parents And there are many other Aayat and Mutawaatir Ahaadeeth which say similar things.
Secondly: obeying and honouring ones parents is a means of entering Paradise, as it was reported in Saheeh Muslim from Abu Hurayrah that the Prophet (peace and blessings of Allaah be upon him) said: He is doomed, he is doomed, he is doomed. It was said, Who, O Messenger of Allaah? He said, The person whose parents, one or both of them, reach old age during his lifetime but he does not enter Paradise.
(Saheeh Muslim, 4627).
Thirdly: Respecting and honouring them brings friendship and love.
Fourthly: respecting and obeying them is a way of showing gratitude to them because they are the ones who brought you into this world. You should also show gratitude towards them for bringing you up and taking care of you when you were young. Allaah says (interpretation of the meaning):
And We have enjoined on man (to be dutiful and good) to his parents [Luqmaan 31:14]
Fifthly: if a person honours his parents this may be the cause of his own children honouring him. Allaah says (interpretation of the meaning):
Is there any reward for good other than good? [al-Rahmaan 55:60]
And Allaah knows best.