Built with a dedicated particle plugin (Trapcode Particular) or After Effects' built-in CC Particle World. Setting the emission angle to a full 360° and adding a little randomness to velocity — so particles travel different distances — is what sells the "burst" feeling.
Three parameters do the real work: how many particles fire at once (the burst count), how fast they spread (velocity), and how fast they fade (life and fade-out). The mix of those three is the difference between a light sparkle and a heavy explosion.
The burst has to peak on the exact frame the logo or title appears — nail that and the two read as one event; miss it and the particles and the title look like two unrelated layers.
When to use
Pull the particle colors from the brand palette — rainbow-colored particles almost always clash with brand tone.