The term used for "treasures on earth" typically refers to riches—both money and material possessions, and that makes sense, since Jesus mentions things that can be stolen by thieves and stuff that can break, rot, or rust. But I think it's fair to extrapolate "treasures on earth" to include anything temporal that we place value in, like Paul mentioning his heritage, education, and status (Phil. 3.4-6) and even worldly pleasures (Eccl. 2.1; Lk. 8.14; Titus 3.3; Heb. 11.25; James 4.3)—a common New Testament competitor for the things of God. This is not to claim there is anything wrong with heritage, education, and even pleasure. But these things are not where we will find the value of life.
To define "treasures in heaven," then, we would need to look for the things Jesus says are of ultimate value. They would include things like...
- Living by the Word of God (Mt. 4.4)
- Trusting God (Mt. 4.7)
- True adoration and exaltation of God (Mt. 4.10)
- Turning away from sin (Mt. 4.17)
- Follow Jesus, meaning do His will and model your life after His (Mt. 4.19)
- Make disciples of others (Mt. 4.20)
- Poor in spirit (Mt. 5.3)
- Hunger and thirst for righteousness (Mt. 5.6)
Etc. You can see where this is going: The treasures in heaven are the inner, spiritual qualities of a believer, conforming to God’s character (Eph. 5.1), being like Jesus (Rom. 8.29), and loving God and loving neighbor.