Any spoken sound that is characterised by an articulation with a closure or narrowing of the vocal tract, resulting in a complete or partial blocking of the flow of air, such as the sounds t, g, f, or z.
Hearing English consonant sounds clearly and then practising them a lot is the greatest method to learn them. Cambridge English has a number of excellent consonant movies. Close-ups of the mouth are included as they pronounce the sounds, so you may work on your mouth form as well.
Most English accents have 24 consonant sounds, which are represented by 21 letters of the English alphabet (sometimes in combination, e.g., ch and th).