Doesn't make much sense to me...

Say the particle is 'watching' a clock. It normally lives for one minute, say from 12.00 to 12.01. However at near light speeds, the time of its surroundings goes faster; it still experiences itself as living for one minute, however it sees the clock go from 12.00 to say 13.00 in this minute. Therefore external observers see the particle for a whole hour.