Apricot Kernels can taste like Almonds, to which they are closely related, because they contain benzaldehyde, the same chemical which gives Almonds and imitation Almond extract their flavour. Apricot Kernels are dangerous, however: see the nutrition section below.
Substitutes
In Asian recipes, substitute Almonds, which are safe to eat, for Apricot Kernels.
Nutrition
Like bitter Almonds, Apricot Kernels are poisonous until heated or roasted, because they contain small amounts of cyanide. Accidentally eating a raw kernel or exposing it to the fruit by a cracked stone is not going to harm anyone; but 10 raw pits are estimated to be enough to kill a small child. In short, let commercial processors process them safely; at home, just discard.
Despite that, the kernels are widely sold and eaten in Asian cultures. And, because the kernels (especially raw kernels) contain Vitamin B17 (laetrile), which some people consider an aid to cancer treatment, they are becoming popular as an alternative cancer therapy amongst some in the West. Sale of the raw kernels, though, is banned in many Western countries.