So I read the posts regarding the MLE and I'm confused:
All right, I'm going to tackle these, but note that the first and last questions are actually a bit contradictory.
Why is it important for the Kings to be under the cap before the season begins?
The beginning of the (playing) season is not really important, as the vast majority of free agency activity (including all desirable players) occurs before then. The NBA season technically begins on July 1st, although there is a brief moratorium during which players and teams can discuss contracts but those contracts cannot actually be signed. Contracts can begin to be signed on July 10th.
If the Kings are under the cap on July 10th, they can spend up to the cap on other teams' free agents. Those free agents include, but are not limited to, Chris Paul and Dwight Howard. Having "cap space" is a fundamental part (but only a part) in the ability to spend money on free agents. The Kings currently have about $42M in salaries committed for next year, not counting the $2.4M that will be owed to the #7 pick. Because the salary cap is expected to be about $58M, the Kings will have the ability to spend up to $13.5M* on other teams' free agents.
*The asterisk is there because the situation is a bit more complicated that that. For one, any money that the Kings spend on their own free agents (for instance, Tyreke Evans) would be subtracted from that cap space number. Cap holds are another complication, which I will explain in turn.
Also note that the $13.5M can be augmented by another exception - an extra $2.65M (the "Room exception"), though this cannot be combined with the cap space. Thus, if we did not re-sign Evans or any other or of own free agents, we could spend up to $16M on other teams' free agents without having to shed salary elsewhere. However, that $16M could not be spent on a single player, because the $2.65M chunk and the $13.5M chunk have to be spent separately.
The Kings could also clear additional cap space by two other methods. 1) They could trade away players and receive lower-salaried players in return. 2) They could amnesty John Salmons. Under the amnesty rules, Salmons is the only reasonably eligible Kings player for amnesty. (Technically DeMarcus Cousins is also eligible for amnesty but nobody would dream of actually doing that.) If Salmons is amnestied, the Kings acquire about $7.6M in cap space (that is equal to Salmons' salary - however they would still have to PAY Salmons' salary, it would just not count against their cap number).
What does it matter what Tyreke's cap hold is?
Cap holds are a crucial part of the salary cap calculation. A cap hold gives a team the right to exceed the salary cap to sign their own free agents. I don't want to go into the details of which free agents get cap holds and how large the cap holds are, but for example the Lakers have a $20.5M cap hold for Dwight Howard despite already being over the cap, having $80M in salary committed next year. This means that the Lakers can go up to $100.5M to sign Howard if they want to. The Hawks would also be able to offer Howard $20.5M dollars even though they do not have a cap hold for Howard (he's the Lakers' free agent, not theirs), because they have something near $40M in cap space. The Kings, however, cannot currently offer Dwight Howard that much money because they do not have enough cap space.
Tyreke's cap hold is actually about $13M, which turns out to be about the same size as our maximum cap space. We can use some or all of that cap hold to sign Tyreke, or we can renounce the cap hold if we want to spend that money on another team's free agent (with the consequence that we then can't spend that money on Tyreke). Currently we have a maximum of $28.5M in free agent cap holds distributed among Tyreke, James Johnson, Toney Douglas, and Cole Aldrich. You'll note that the sum of these cap holds takes us well over the salary cap. This is important, because it means that unless we renounce some of these cap holds, we are over the salary cap and can't spend (much) money on other teams' free agents.
We are widely expected to renounce the cap holds for Johnson, Douglas, and Aldrich, leaving us only Tyreke's cap hold. Since that cap hold is slightly less than our salary cap space, the existence of the cap hold is not terribly important for us if we want to sign Tyreke - we could sign him with our hold, or with our cap space. However, the cap hold would still prevent us from signing another team's free agent for any significant amount of money.
Once he's signed or traded, that goes away, right?
Yes. If Tyreke signs with the Kings, his cap hold is replaced by the actual value of his salary. Most people expect that his salary will be a bit lower than his $13M cap hold, but I do not personally believe that his salary will come in below $11M wherever he signs.
If Tyreke signs with another team, his cap hold goes away entirely. It should be noted that we will have some control over whether or not Tyreke signs with another team. This is because Tyreke is at the end of his rookie contract, which means that we can make him a "restricted free agent" by tendering a qualifying offer. For Tyreke the QO is just under $7M and there is little doubt that we will tender it. Once the QO is tendered, Tyreke is free to seek out the best contract he can find among the other 29 teams, but we have the right to match it, no matter what it is (even if it exceeds the cap hold) and retain him.
Tyreke can only be traded in a sign-and-trade. In that case, we would be getting contracts back from the team that signed him. Tyreke's cap hold would go away, but it would be replaced by the contract(s) we acquired.
Why do we care if the Kings qualify for a MLE so many months before the season begins?
Again, the MLE is important starting July 1st and has less importance towards the beginning of the playing season as available free agents sign with other teams. The MLE is important because it is bigger than the "Room exception" - almost twice as big as a matter of fact. This year, the MLE is slightly larger than $5M. The MLE would give us the ability to sign another reasonably good player in addition to Tyreke. However, given that we are expected to renounce our cap holds on our other players, if we do not succeed in signing Tyreke we will lose our MLE. This is because the sum of our salaries ($44.5M), our cap holds (in this scenario, $0) and our exceptions (the MLE at $5M and the Bi-annual at $2m) would be about $51.5M, below the cap. Once such a scenario happens, the exceptions are lost. That's just the rules.
I hope this made at least some sense.