What does it mean to observe times in the Old Testament?

Answer 1

From Leviticus 19:26 where the statement Observe Times is mentioned

That phrase means the following in the Hebrew (according to the Strong's concordance dictionary)

Hebrew Word # 06049 // Nne // `anan // aw-nan' //

a primitive root; TWOT - 1655,1656; v

AV - observer of times 5, soothsayer 2, bring 1, sorceress 1,

enchanter 1, Meonenim 1; 11

1) (Piel) to make appear, produce, bring (clouds)

2) (Poel) to practise soothsaying, conjure

2a) to observe times, practice soothsaying or spiritism or magic

or augury or witchcraft

2b) soothsayer, enchanter, sorceress, diviner, fortuneteller,

barbarian, Meonenim (participle)

Answer 2

For Jews, it means to observe (to keep and fulfill) the festivals. See also:

Festivals and other occasions