What does "convey/possess a sense of immediacy" mean?

Such contemporary accounts often convey a sense of immediacy and impact...

The opening pages still convey a sense of immediacy and excitement...

The challenge of the environmental beat is to convey a sense of immediacy and pertinence...

Importantly, these acts possess a sense of immediacy...

Photographic images usually possess a sense of immediacy...

The new issues addressed in this edition possess a sense of immediacy...


Solution 1:

convey a sense of immediacy

The subject (contemporary accounts, opening pages, etc.)

  • expresses a direct influence on the reader, and/or
  • expresses an urgent call to action (mostly in a practical sense).

whereas

possess a sense of immediacy

leans more towards the first meaning.