What does it mean to not touch the Lord's anointed?

from the old testament

• In the Old Testament, to anoint someone referred to God’s authority being established over one who held a particular position. It was not done just for kings but also for others, such as priests (Exodus 29:7).
• In the case of Saul, God anointed him to be the first king of Israel (1 Samuel 10:1). After he sinned (1 Samuel 15:26), however, God anointed David in his place (1 Samuel 16:13). Later, after placing David in his army, he became jealous of the praise David received (1 Samuel 18:6–9) which festered until David had to flee for his life (1 Samuel 19:12). Knowing that David was his successor (1 Samuel 23:17), Saul soon followed after Him to kill him (1 Samuel 23:25).
• At one point during the pursuit, David and his men were hiding in a cave. Saul, not knowing that, went into the cave to “relieve himself” (1 Samuel 24:3). With his guard down, David’s men told him that the Lord must have given Saul into his hands and so he should kill him (1 Samuel 24:4).
• David responded by saying, “The LORD forbid that I should do this thing to my lord, the LORD’s anointed, to put out my hand against him, seeing he is the LORD’s anointed” (1 Samuel 24:6. See David’s similar statement later in 1 Samuel 26:8).
• What David was saying was that because God had anointed Saul, only God could judge Saul. God had not given David permission to be His executioner. Thus, had David killed Saul, it would have been an act of personal vengeance, not a righteous, God-honoring one. He allowed Saul to go, knowing that God would eventually remove Saul from power in His timing.

from the new testament

• Some today have misused 1 Samuel 24:6 and 1 Samuel 26:8 to claim that a particular leader is above reproach. It is generally phrased along the lines of “touch not God’s anointed!” However, in context, those passages were about the execution of final judgment (death) upon men whom God had clearly anointed. In the New Testament church, no spiritual leader is above rebuke or even removal.
• Indeed, the qualification for a leader, among other things, is that he is above reproach (1 Timothy 3:1–7, Titus 1:6–9). Being “above reproach” means not doing or saying anything that would disqualify him from leadership, such as promoting serious doctrinal error.
• Even the original apostles were not above rebuke when they strayed. An example of this is when Peter (known as Cephas) “stood condemned” for trying to please the Jews by withdrawing from fellowship with Gentiles (Galatians 2:11–12). This hypocrisy affected not just Peter but those around him, so Paul publicly rebuked him (Galatians 2:13–14). If an apostle could be corrected for doctrinal error, then no one is “untouchable.”

implications for today

Contextually, the statement about not touching God’s anointed was very specific and about David’s refusal to kill the king God had anointed. David understood that he, as a man, didn’t have the authority to kill God’s authorized king.

In modern times, that statement has been taken out of context to mean that certain spiritual leaders are “untouchable,” meaning their authority or teachings should never be questioned. It’s akin to throwing up a spiritual shield as a blanket defense for all a particular leader says and does.

While Scripture does teach that we are to respect those in authority over us (Hebrews 13:17), it also teaches that Scripture, not any leader, has the final authority (2 Timothy 3:16–17). If anything or anyone contradicts it, then that thing or person must be corrected.

While some well-meaning teachers may use this verse, it’s generally used by those who cannot otherwise defend themselves against an examination by Scripture. That is, it protects them against closer examination by accusing the other person of attacking God’s specially called leader. Thus, caution should be exercised in listening to anyone who makes this claim for themselves or another, as it is a sign that they are not living in accordance with God's ways.