It is imperative to read and understand verse 10 in conjunction with verse 11. Peter just concluded that salvation is provided only to believers by God's grace through their faith. Those prophets, inspired by the Holy Spirit of God, predicted the coming grace of God for those in the time of Peter (and ours). Following this, the prophets searched and asked questions, hoping to gain a better understanding of the writings. What they were seeking is specifically described in verse 11.
In history, many prominent prophets, such as Daniel and Isaiah, Jeremiah, Zechariah, and Malachi, yearned to understand the salvation they preached about. However, much of what they saw was hidden from their eyes. When they predicted the sufferings of the Messiah and the glory that would follow, they longed to discover what era or specific time the Spirit of the Messiah, in them, was referring to.
However, we have been provided with all we need for life and godliness during this Church dispensation. Let us study so that we will be approved as believers. This will ensure that in these end times, we are not tossed about by every wind of doctrine, nor will we be misled by false prophets or false teachings. Let us look to Jesus for guidance. Let us place our faith in Him and use His holy Scriptures as a guide to finding the truth.

Dear Heavenly Father, it is Your gracious mercy that You have revealed to us all what we need for life and godliness in Christ Jesus, our Savior. Please bless us with wisdom and understanding in this increasingly evil world, and may we be satisfied with all that You have revealed to us in Your Word, and not try to discover any secret knowledge that You in Your wisdom have chosen to keep hidden from us. 
In Jesus's name I pray. Amen.