This feat, as long as they are already a caster class like bard, gives the player two additional cantrips. They are allowed to pick a casting class, even if it is not their own, and take two cantrips from its spell list. They can also learn an additional level 1 spell from that class's list. This feat can be very helpful for classes such as bards that learn spells as they go and have a limited number they are allowed to know.
The spell casting ability for the cantrips and spells learned corresponds to whatever class they borrowed the spells from. The 1st level spell can only be used once per long rest, but the cantrips function regularly. The Magic Initiate feat can save a player the hassle of having to multiclass in order to gain a few low-level spells they want from another caster class.