A counterspelled spell has no effect, and a spell's effect is its description.
Counterspell says:
its spell fails and has no effect.
The effect of booming blade is exactly its spell description:
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, the target suffers the attack’s normal effects, and it becomes sheathed in booming energy until the start of your next turn. If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends.
The entire description of booming blade is the spell's effect. This is stated explicitly in the rules for spellcasting:
Each spell description in Chapter 11 begins with a block of information, including the spell's name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell's effect.
Therefore, if booming blade is counterspelled, it has no effect, meaning everything in the spell description does not happen, since the spell description is that effect. The effect of a successfully counterspelled booming blade is:
There is no effect.