The neglected paradox
Great answer by @Jack Douglas, I agree with him in all he says. Yet, even he does not specially discuss the most paradoxical and intriguing words of this passage, namely
"but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared.” (Mark 10:40).
Below, I shall discuss and explain why is this logion paradoxical and what is the theologically sound exegesis of it.
What is paradoxical here? This is what: Jesus, in fact, states that He is powerless to grant the level of proximity of His followers to Him. Now, any earthly king has this power to make somebody a chief minister, closest to him, so why Jesus, the Heavenly King (John 18:36) is devoid of this capacity? (To anticipate things later below to be explained: just because He is heavenly and not earthly king!). But who is then more powerful than He, who has prepared this proximity for His followers, for it is plainly written that "those places have been prepared for some", but if Jesus Himself was who has prepared, then He also has granted, for the first implies the second. But Jesus necessarily denies the first (i.e. preparation) while denying the second (i.e. granting). So, who then has prepared those places if not Jesus? Who is this more powerful principle, against whom even Jesus has to confess His powerlessness? Maybe the Father? Maybe the Father has prepared saints' proximity to His Son and the latter cannot change any more what the Father has prepared. But this answer is theologically totally unsound, for Father acts His deeds only through the Son (creates the universe through His Son/Logos; forgives sins and saves mankind through the Son/Logos etc.,), thus if the Father has prepared and granted, then necessarily also the Son has likewise and simultaneously prepared and granted, but Jesus denies it for Himself, and by implication, also denies it for the Father. Of course, neither Holy Spirit can be this "preparer" and "grantor" against whom neither Father nor Son can do anything (I will not develop logic for proving this last point, for it will be redundant). Thus, the Trinity does not prepare and grant the greater or lesser proximity to the hypostasis of the Son, the incarnate Logos Jesus Christ, and, therefore, even the Trinity is powerless to grant this grater or lesser proximity. But Trinity is God and as God is omnipotent, so what is this principle against which even God is powerless? Maybe Fate? There is Trinity, yes, but alongside with the Trinity there could be also the Fate/Necessity (Τυχή/Ἀνάγκη) which sets things in such a way that even the Trinity cannot change it. But this is absurd, for then instead of the Biblical omnipotent God we shall obtain a pagan deity like Zeus who is weaker than Fate/Necessity in Greek religion and start henceforth building temples to Lady Fate/Necessity and worship her alongside or even more principally than the Trinity. Thus, to avoid this absurdity, we must conclude that neither fate/necessity prepares and grants saints' degrees of proximity with Jesus. But then what?
And here comes the answer: nothing but human freedom, in which even God does not intervene; for nothing but human freedom can decide the intensity of human co-action with divine Grace; nothing but human freedom can decide how much alike Christ to become, how closely imitate Him, how heavy a cross to carry, how many needful neighbours to help. God gives talents, that is to say apportions His Grace to humans, but say, Chuck, out of his free initiative, increases those talents more, while, say, Jonathan, again out of his free initiative, also increases, but less so than Chuck, and both are very good Christians, faithful custodians of Grace, but with greater or lesser reciprocation with God and greater or lesser free efforts and exertion. But proximity with God is exactly pending on this free initiative, free reciprocation with Him and free exertion. But against our freedom even God made Himself utterly powerless, because He utterly respects it in us, for it is the mark of His image and likeness in us, for without this intrinsic gift in us, we are even not humans any more and this gift of free decision-making is as intrinsic and inseparable from us as thinking is four our minds and as ability to breathe is for our bodies until they are alive and breathe. As a beautiful image tells about divine and human interaction: Jesus stands and knocks constantly to the door of our hearts, but this door has only one handle, that from inside, so even Jesus cannot break in, so to say, into our hearts without us freely letting Him to, freely and with a reciprocal desire opening our heart's door to Him with the handle of our free choice, which only we can stir. And that is exactly why the earthly kings can, in fact, make anybody, any wretch and undeserving person to sit in a closest proximity to his throne out of his sovereign initiative, but Jesus as the Heavenly King is unable to do so, for even though He desires all to come to Him most closely, He cannot impose this and cannot make an unwilling or un-reciprocating person "sit" close to Him even by His Sovereign Authority, for it was exactly by this Sovereign Authority that He gave to us, humans, this untouchable freedom of free will, free choice and the ability of free decision-making.
Thus, to conclude: Jesus' words express a divine respect towards an awesome, a horrible gift of freedom (and therefore, also the horrible responsibility) that all humans, as images and likenesses of God, have been endowed by Him. We can use this gift for following sins and making ourselves remote from God, or we can use this gift for repenting and making ourselves closer to God, or, moreover, we can use this gift for even greater opening of our hearts and lives to the infinity of divine love towards us and get even closer to Him, but He does not force us, it is only on us and our free, dreadfully so, decision.
Jesus speaks about the mystery of human freedom in this passage.
