The word ‘Martyr’ in Greek really means witness. I was reading from the book Extreme Devotion published by the Voice of the Martyrs (VOM) and I felt that in one of the first pages of the book, in fact one of the very first pages which reads “This books is dedicated to …” the definition of a martyr is well said.

those who chose death over denial …
who chose faith over fear …

and chose to be a witness rather than walk away.
For all those of whom the world was not worthy (Hebrews 11:38).

Summarizing, a martyr is one whose choice far exceeds anything the world can afford to give.
To be a martyr (witness) for Jesus Christ is a matter of choice!

Choose you this day, whom ye will serve but as for ME and MY HOUSE, we will serve the LORD (Joshua 24:15)

Hebrews 11:35 (KJV)
35
…  and others were tortured, not accepting deliverance; that they might obtain a better resurrection:
36
And others had trial of cruel mockings and scourgings, yea, moreover of bonds and imprisonment:
37
They were stoned, they were sawn asunder, were tempted, were slain with the sword: they wandered about in sheepskins and goatskins; being destitute, afflicted, tormented;
38
(Of whom the world was not worthy:) they wandered in deserts, and in mountains, and in dens and caves of the earth.

39
And these all, having obtained a good report through faith, …