What many of the Old Testament prophets and the righteous wanted to see and hear was the coming of Christ and the completion of Christ’s work. Jesus explains to the great crowd by the sea that what they see and hear is what the prophets and the righteous wanted to see and hear. That is, many prophets and righteous people wanted to see and hear the ministry of Christ coming and showing Himself as the Christ.
Mt 13:16 But blessed are your eyes, for they see: and your ears, for they hear.
17 For verily I say unto you, That many prophets and righteous men have desired to see those things which ye see, and have not seen them; and to hear those things which ye hear, and have not heard them.
The forefathers of the Old Testament believed in the coming of Christ and gained evidence by wishing.
Heb 11:1 Now faith is the substance of things hoped for, the evidence of things not seen.
2 For by it the elders obtained a good report.
Heb 11:39 And these all, having obtained a good report through faith, received not the promise:
John testifies that we have heard the word of life from the beginning, and now we directly heard it, saw it with our own eyes, and touched the One whose word had become flesh. That is Jesus.
1 Jn 1:1 That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life;
2 (For the life was manifested, and we have seen it, and bear witness, and shew unto you that eternal life, which was with the Father, and was manifested unto us;)
In conclusion, it was Christ that many prophets and the righteous wanted to see and hear.