Paul said, "I do not want you to be ignorant of this mystery, brothers and sisters, so that you may not be conceited: Israel has experienced a hardening in part until the full number of the Gentiles has come in," (Romans 11:25). Barnes Notes explains the word 'mystery' thus:
"Ignorant of this mystery - The word "mystery" means properly what is "concealed, hidden, or unknown." And it especially refers, in the New Testament, to the truths or doctrines which God had reserved to himself, or had not before communicated. It does not mean, as with us often, that there was anything unintelligible or inscrutable in the nature of the doctrine itself, for it was commonly perfectly plain when it was made known. Thus, the doctrine, that the division between the Jews and the Gentiles was to be broken down, is called a mystery, because it had been, to the times of the apostles, concealed, and was then revealed fully for the first time."
Paul was explaining to the Jews that though the Gentiles were now coming in, God would not forsake the Jews totally. After all, Paul said Jesus had saved Paul, hadn't He? It wasn't over for the Jews, but Paul did remind them that God was now rejecting a large part of the nation because of their past rebellion. His attention and grace would be showered on the Gentiles, who were being grafted in. The Jews would remain hardened of heart - until the full number of Gentiles was met. But just as God had always done in the past, a remnant would be saved.
The Jews would receive their Kingdom as promised, but their entry into it must as always be by faith through His grace, not birthright. As for us today who have claimed salvation through Jesus - Whom we recognize as our Messiah - we will continue in the Church Age until the full number is filled and then we fly. It is why the rapture isn't a date, it is a number. It will not be May 21, unless that is the day that God has deemed the Church quota filled.
The second thing Paul said not to be ignorant about is spiritual gifts. "Now concerning spiritual gifts, brethren, I do not want you to be ignorant:" (1 Corinthians 12:1-3). Paul was reminding the Church of the importance of the gifts, through which we accomplish the work the Holy Spirit wants us to accomplish to build up the church. (1 Corinthians 14:12) The gifts are important, they are given (which is a grace and a blessing) to build up the church (ditto) and they grow the Christian himself as well (bonus). Bible.org explains, "a spiritual gift is the supernatural ability to carry out the work of Christ through his church."
And yet the spiritual gifts doctrine is precisely what many people are mixed up over. 'You must speak in tongues or you're not a real Christian." "What's my spiritual gift, let me take this questionnaire." People certainly are ignorant of the gifts, sad to say. Satan did a good job of mixing us all up on that. If we are mixed up as to the truth of the spiritual gifts, then we are not as effectively building the church, are we?
Thirdly, Paul warned the church not to be ignorant of the doctrine of Last Days and the Coming of The Lord. "But I do not want you to be ignorant, brethren, concerning those who have fallen asleep, lest you sorrow as others who have no hope." (1 Thessalonians 4:13)
Jamieson-Fausset-Brown Bible Commentary explains:
"The leading topic of Paul's preaching at Thessalonica having been the coming kingdom (Acts 17:7), some perverted it into a cause for fear in respect to friends lately deceased, as if these would be excluded from the glory which those found alive alone should share. This error Paul here corrects."
What are the exact three things the Church is ignorant of? What are most arguments over these days? The rapture doctrine and what is forecast for Israel, the spiritual gifts doctrine (speaking in tongues and healing gifts, and the Charismatics, for example) and the doctrine of the Coming of the Lord.
Paul said do not be ignorant three times, and yet in this day and age so many people are three times as ignorant as they ever were.
A solution for ignorance is available. The Spirit. He helps interpret scripture: 1 Cor. 2:1,14; Eph. 1:17. If your house was on fire, you would call the fire department for help, wouldn't you? If a robber was breaking into your house, you would call the police department wouldn't you? Both are dire circumstances, signifying events that need an authority of higher power and skill to help you. And yet we so often fail to call the Holy Spirit, our higher authority possessing more skill and knowledge to bring to the situation than we could ever hope to see anywhere! Praise Him. Here is a good page outlining the ministry of the Holy Spirit.
Ignorance leads to error. "Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God." (Matthew 22:29) Call on Him through prayer, and abide in the Spirit's power: "But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you." (Romans 8:11)