This section explains what happens when double bonds — or a double bond and an adjacent reactive center — are positioned so their p orbitals can overlap and share electrons across more than two atoms. That sharing is delocalization, and it is the single organizing idea behind everything in this cluster.

Start with the three ways two double bonds can relate in a molecule:

Conjugated dienes have alternating double and single bonds (C=C–C=C). The p orbitals are aligned across all four carbons, so the pi electrons delocalize. This is the most stable arrangement.
Isolated dienes have the double bonds separated by two or more sp³ carbons (C=C–C–C=C). They behave like two independent alkenes.
Cumulated dienes (allenes) have two double bonds on one carbon (C=C=C). These are the least stable and are a special case.

The stability ranking — conjugated > isolated > cumulated — is measured by heats of hydrogenation: a conjugated diene releases less heat than expected, and that deficit is the resonance (delocalization) stabilization energy. Conjugation also has structural fingerprints: the central C–C "single" bond of 1,3-butadiene is shorter than a normal single bond because it has partial double-bond character, and the whole conjugated system prefers to be planar so the p orbitals stay aligned.

The allylic system is the second half of this section and the most testable. An allylic position is the sp³ carbon next to a double bond. When a cation, radical, or anion forms there, it is resonance-stabilized because the adjacent pi bond delocalizes the charge or unpaired electron across two carbons:

The allylic carbocation is far more stable than a comparable non-allylic cation (a primary allylic cation rivals a secondary). This stability is why allylic systems are so reactive in SN1/E1 chemistry.
Because the positive charge is spread over two carbons, a nucleophile can attack at either end, giving two products. This is the origin of 1,2- vs. 1,4- (conjugate) addition to dienes.

That last point is a classic exam contrast. When HX or a similar reagent adds to a conjugated diene, the intermediate is an allylic cation, so you get:

1,2-addition product — favored at low temperature (kinetic product); it forms faster because the nucleophile attacks the closer, more stabilized carbon.
1,4-addition product — favored at high temperature (thermodynamic product); it is more stable because it retains the more substituted internal double bond.

This is the canonical illustration of kinetic vs. thermodynamic control: the same starting materials give different major products depending on temperature (and reversibility), because the faster-forming product is not the most stable one.

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