From BiblePortal Wikipedia

King James Dictionary [1]

Observe obzerv'. L. observo ob and servo, to keep or hold. The sense is to hold in view, or to keep the eyes on.

1. To see or behold with some attention to notice as, to observe a halo round the moon I observed a singular phenomenon we observe strangers or their dress. I saw the figure, but observed nothing peculiar in it. 2. To take notice or cognizance of by the intellect. We observe nice distinctions in arguments, or a peculiar delicacy of thought. 3. To utter or express, as a remark, opinion or sentiment to remark. He observed that no man appears great to his domestics. 4. To keep religiously to celebrate.

A night to be much observed to the Lord.  Exodus 12 .

Ye shall observe the feast of unleavened bread.  Exodus 12 .

Ye observe days, and months, and times, and years.  Galatians 4 .

5. To keep or adhere to in practice to comply with to obey as, to observe the laws of the state to observe the rules and regulations of a society.

Teaching them to observe all things whatsoever I have commanded you.  Matthew 28 .

6. To practice.

In the days of Enoch, the people observed not circumcision or the sabbath.

OBSERVE, observ'.

1. To remark. I have heard the gentleman's arguments, and shall hereafter observe upon them. 2. To be attentive.

Webster's Dictionary [2]

(1): ( v. t.) To take notice of by appropriate conduct; to conform one's action or practice to; to keep; to heed; to obey; to comply with; as, to observe rules or commands; to observe civility.

(2): ( v. t.) To express as what has been noticed; to utter as a remark; to say in a casual or incidental way; to remark.

(3): ( v. i.) To take notice; to give attention to what one sees or hears; to attend.

(4): ( v. t.) To be on the watch respecting; to pay attention to; to notice with care; to see; to perceive; to discover; as, to observe an eclipse; to observe the color or fashion of a dress; to observe the movements of an army.

(5): ( v. i.) To make a remark; to comment; - generally with on or upon.

Hastings' Dictionary of the Bible [3]

OBSERVE .   Mark 6:20 ‘Herod feared John, knowing that he was a just man and an holy, and observed him.’ The meaning of the Eng. word ‘observed’ is ‘reverenced.’ Tindale’s translation is ‘gave him reverence.’ Cf. Shaks. 2 Henry IV . iv. iv. 30, ‘he is gracious, if he be observed.’ But the more probable meaning of the Greek is ‘protected him,’ or, as RV [Note: Revised Version.] , ‘kept him safe.’

International Standard Bible Encyclopedia [4]

ob - zûrv ´ (representing various words, but chiefly שמר , shāmar , "to keep," "to watch" etc.): Properly means "to take heed to," as in   Isaiah 42:20 , "Thou seest many things, but thou observest not" and from this sense all the usages of the word in English Versions of the Bible can be understood. Most of them, indeed are quite good modern usage (as "observe a feast,"  Exodus 12:17 , etc.; "observe a law"  Leviticus 19:37 , etc.), but a few are archaic. So  Genesis 37:11 , the King James Version "His father observed the saying" (the Revised Version (British and American) "kept the saying in mind");  Hosea 13:7 , "As a leopard ... will I observe them" (the Revised Version (British and American) "watch");  Jonah 2:8 , "observe lying vanities" (the Revised Version (British and American) "regard," but "give heed to" would be clearer; compare  Psalm 107:43 ). Still farther from modern usage is  Hosea 14:8 , "I have heard him, and observed him" (the Revised Version (British and American) "will regard"; the meaning is "care for"); and  Mark 6:20 , "For Herod feared John ... and observed him" (the Revised Version (British and American) "kept him safe"). In the last case, the King James Version editors seem to have used "to observe" as meaning "to give reverence to."

Observation is found in   Luke 17:20 , "The kingdom of God cometh not with observation" (μετὰ τηρήσεως , metá paratērḗseōs ). The meaning of the English is, "so that it can be observed," but the exact force of the underlying Greek ("visibly?" "so that it can be computed in advance?") is a matter of extraordinary dispute at the present time. See Kingdom Of God .