Do readied spells take effect?

It's in the PHB

Under Spellcasting:

A spell is a discrete magical effect, a single shaping of the magical energies that suffuse the multiverse into a specific, limited expression. In casting a spell, a character carefully plucks at the invisible strands of raw magic suffusing the world, pins them in place in a particular pattern, sets them vibrating in a specific way, and then releases them to unleash the desired effect — in most cases, all in the span of seconds.

And under Ready (combat action):

When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell's magic requires concentration (explained in chapter 10).

The spell must have a casting time of one action, so spells that take longer, or are bonus actions are disqualified. So are reactions, but they already have a trigger.

So per the description, the caster shapes magical energy which normally takes a single action. But in this case, you hold that energy (which is the magic). Once the trigger occurs you can release the energy (or you lose concentration and the energy dissipates without effect).

The other key is that you "release with your reaction". Except under edge cases, the character's reaction does not happen on their turn. It happens as a trigger to someone else's turn. So there is a built-in delay; cast on your turn and release on someone else's.