user91152: Public key tweaks are often talked about in the context of taproot but I cannot find a definition of what precisely "tweaking" means.

user47827: The Bitcoin Optech Taproot workshop defines it as:

Tweaking a public key means to alter it with a value (the tweak) such that it remains spendable with knowledge of the original private key and tweak.
A tweak is positive scalar value t where 0 < t < SECP256K1_ORDER. There is an associated tweak point T such that T = t*G. The private key is tweaked by the tweak scalar: x' = x + t and the public key is tweaked by the tweak point: P' = P + T.
The tweaked private key x' can be used to produce a valid signature for the tweaked pubkey P'.


91152: <p>Public key tweaks are often talked about in the context of taproot but I cannot find a definition of what precisely &quot;tweaking&quot; means.</p>
 47827: <p>The Bitcoin Optech Taproot workshop <a href="https://github.com/bitcoinops/taproot-workshop/blob/master/2.2-taptweak.ipynb" rel="nofollow noreferrer">defines</a> it as:</p>
<blockquote>
<p>Tweaking a public key means to alter it with a value (the tweak) such that it remains spendable with knowledge of the original private key and tweak.</p>
<p>A tweak is positive scalar value <code>t</code> where <code>0 &lt; t &lt; SECP256K1_ORDER</code>. There is an associated tweak point <code>T</code> such that <code>T = t*G</code>. The private key is tweaked by the tweak scalar: <code>x' = x + t</code> and the public key is tweaked by the tweak point: <code>P' = P + T</code>.</p>
<p>The tweaked private key <code>x'</code> can be used to produce a valid signature for the tweaked pubkey <code>P'</code>.</p>
</blockquote>
