In context of long distance running, strength means ability to hold your pace for longer time.
It is essentially how good your speed at lactate threshold is relative to your event and others at your event. Some people use the words "stamina" or "endurance" for the same concept, which leads to a lot of confusion.
When someone says runner X is very strong in 10k, it means his speed is lacking (relatively, for 10k), but his strength/endurance/stamina makes up for that, so that he would run much better half than 5k, even though 10k could be his best event. In that half he would probably be considered not "strong", but "fast". So it's all relative.
TLDR: Strength training is essentially LT training, 10k pace and slower.