of great worth: costly and highly valued when it is a thing, honored and esteemed when it is a person
The word comes from τιμή, the noun for worth, price, or honor, and it presses that whole idea into a single adjective: to be timios is to count for a great deal. Most often the New Testament uses it for things of high material value: the precious stones and costly wood of a merchant's cargo, the gold and jewels of a great city, and, by extension, things whose worth is not measured in money at all, such as the blood of Christ, the farmer's long-awaited crop, God's promises, and even a person's own life.
The same adjective also describes a person or an institution held in honor. The teacher Gamaliel is spoken of this way, respected by all the people, and marriage is to be treated as honorable and worthy of respect by everyone. Here English reaches for "honored" or "esteemed" rather than "precious," but the underlying idea is unchanged: this is something of real worth that should be treated accordingly.
Greek has a small family of related words for worth and honor. πολύτιμος sharpens the idea to "very costly," used of the pearl worth a fortune, while ἔντιμος leans toward being prized or held in honor. This word is the plain, general term in the middle: worth a great deal.