Explaining 2 Corinthians 11

In 2 Corinthians, Paul writes primarily for the purpose of defending his apostolic authority to the church in Corinth in the face of false accusations made against him by false apostles. Paul had previously written a strong letter to the church rebuking them for various misbehaviors (1 Corinthians), and his rebuke hurt the feelings of church leaders. This gave opportunity for false teachers to undermine Paul in his absence and introduce false teaching. 

Paul responds to this threat with great humility in 2 Corinthians to reassure the church of his love for them and of his apostolic authority from Christ, while at the same time contending with the false teachers. At times in the letter Paul acknowledges his weaknesses and faults, yet he also takes a strong stand in denying the false accusations made against him. 

In Chapter 10 Paul argues for their trust by contrasting his humility and God-given authority with his accusers' arrogance and incompetence:

2Cor. 10:12 For we are not bold to class or compare ourselves with some of those who commend themselves; but when they measure themselves by themselves and compare themselves with themselves, they are without understanding.
2Cor. 10:13 But we will not boast beyond our measure, but within the measure of the sphere which God apportioned to us as a measure, to reach even as far as you.

Then in Chapter 11, Paul opens by thanking the church for standing by Paul despite his weaknesses and "foolishness:"

2Cor. 11:1 I wish that you would bear with me in a little foolishness; but indeed you are bearing with me.
2Cor. 11:2 For I am jealous for you with a godly jealousy; for I betrothed you to one husband, so that to Christ I might present you as a pure virgin.
2Cor. 11:3 But I am afraid that, as the serpent deceived Eve by his craftiness, your minds will be led astray from the simplicity and purity of devotion to Christ.
2Cor. 11:4 For if one comes and preaches another Jesus whom we have not preached, or you receive a different spirit which you have not received, or a different gospel which you have not accepted, you bear this beautifully.

Paul says he wishes the church would stand by him despite Paul being foolish at times, which was Paul's humble way of acknowledging that he had sin like everyone (though it was not a concession to the false accusations). Nevertheless, Paul says his motivation has always been a godly jealousy for the church in Corinth to grow spiritually into a spotless Bride presented to Christ, Her Groom, just as God intended. In other words, Paul was using his authority for the right reasons.

On the other hand, Paul said he fears that this young, impressionable church may be deceived in the same way that Eve was deceived in the Garden, by paying attention to demonic temptations to sin rather than remaining devoted to Christ's commands for His Church. While the church had done well to that point in rejecting false gospels preached by false "spirits" (i.e., demonically-influenced teachers), nonetheless Paul worried that the church could allow these false apostles to lead them astray out of spite for Paul. 

So after that Paul moves from v.4 into a defense of his motives as he reminds the church that he came to them humbly preaching without even asking for financial support. Finally, Paul reminds them that his opponents were not so pure:

2Cor. 11:13 For such men are false apostles, deceitful workers, disguising themselves as apostles of Christ.
2Cor. 11:14 No wonder, for even Satan disguises himself as an angel of light.
2Cor. 11:15 Therefore it is not surprising if his servants also disguise themselves as servants of righteousness, whose end will be according to their deeds.