I believe there is more to clarify this statement, as many people jump to conclusions. Under the Islamic principle of a "just war," (which would be things like liberating the oppressed) those who give their lives while fighting and/or defending are considered martyrs
. One who dies the death of a martyr, or shaheed
, is promised Paradise, and basically goes straight in to its highest level without the turmoil and waiting of Judgement Day. It's worth pointing out that those who lead unjust wars or are unrighteous aggressors aren't considered for this privilege.
As to the title, it is a line from a generally accepted hadith. When a sahaba asked the Prophet Muhammad (pbuh) why those people would skip the hearafter's turmoil, he replied because the testing/tribulation of seeing the flashing of swords over ones head was turmoil enough.
That's not to say that under the shade of swords is the only way into Paradise. The Prophet Muhammad (peace and blessings be upon him) also is known to have said, “Paradise is at the feet of the mother.”
“Be at your mother’s feet and there is the Paradise.” (Ibn Majah, Sunan, Hadith no. 2771)