The articulation of consonants differs from that of vowels primarily in the escape of the airstream. While for vowels the air is allowed to escape freely, for consonants there is some sort of stricture at some point in the speech tract. If you compare a vowel like [ɑː] with a consonant like [v], you can get some idea of what is meant by a free escape as opposed to a stricture.
Consonants can be divided, first, on the basis of the type of stricture that occurs: there may be a complete obstruction of the airstream as in the case of [p] and [t], a narrowing, as in the case of [v] and [z], or a near-contact, as in the case of [j] and [w]. If two consonants differ in this respect, i.e. in terms of the way in which the airstream is interfered with, they are said to have a different manner of articulation.
Secondly, consonants may differ in the location of the stricture, in which case we say they have a different place of articulation. This is what makes [p] different from [t], [v] from [z], and [j] from [w].
A third source of variation is the state of the glottis during the articulation of a consonant. It accounts for the difference between [f] and [v] as in surface, service, [p] and [b], as in rapid, rabid, or [k] and [g], as in coal, goal.
For every consonant we can capture these three types of variation in a three-term label. The first term specifies the state of the glottis, the second the place of articulation, and the third the manner of articulation. For [f] as in surface this would be: a voiceless labio-dental fricative.