What does the (P) mean after someones rank? I understand that it means promotable, but what significance does it have?

Attaching tbe (p) to an official signature block can legitimize a decision made by a Soldier of a lower grade that is occupying the slot. For example, some decision may require an O6 signature, but if the approving authority is in promotable status, and is technically still an O5, attaching the - p is used here.

Generally, for most situations, such as a social media site, it is only a source of pride

In my case, it means that you have been selected for promotion to the next rank and you are waiting for the paper train to wind it's way through the system and get promotion orders cut. Personally, I would never refer to myself as MAJ(P). After 16 years, I can wait a couple more months and just change it to LTC.

Being promotable is a status, nothing else. Rank and position matter. For example a SPC holding a NCOIC position will dictate what a SPC(P) has to do.