God Almighty says in the Holy Qur'an: Every soul shall taste death. (Q 3:185) But He says at another place in Qur'an in: Do not say about those who are slain in the cause of Allah, that they are dead. Nay, they are alive, but you do not perceive it. (Q 2:154) Don't both the verses contradict each other?
The verse does not negate the idea that the martyers are dead in the general meaning of the word. It highlights another important thing. It guides us to the fact that life does not end here in this world. It will continue in the afterlife. The Qur'an, in contrast to the life of the martyers, also depics the situation of the rejecters of the truth and the message of God. They are told to be experiencing a kind of punishment. The Qur'an says:
The Fire; they are exposed to it morning and evening; and on the day when the Hour comes [it will be said]: Cause Pharaoh's folk to enter the most awful doom. (Q 40:46)
On the contrary the martyrs and those who pass their life according to the truth are also experiencing a kind of life but that cannot be comprehended by us in this life. That is why the verse says you do not appreciate that they are living and are being fed, as has been explained in the following verse:
Think not of those, who are slain in the way of Allah, as dead. Nay, they are living. With their Lord they have provision. (3:169)
A third group of people who lived a mixed life will however be given life before the Last Day. That is the general orde of happenings. However, the extraordinarily haughty rejecters and the true followers start living a kind of life right after the death.
The verse therefore corrects our conception of the life and death. It says that death does not end life it usheres us into another one.