An affricate is a consonant that begins like a stop (most often [t] or [d]) but ends with a fricative release. The English sounds spelt "ch" and "j" (transcribed [tS] and [dZ]), German z [ts] and Italian z [dz] are typical affricates. These sounds are fairly common in the world's languages, as are other affricates with similar sounds, such as those in Polish and Chinese.
Much less common are labial affricates, such as [pf] in German, and velar affricates, such as [kx] (written kg) in Setswana. Worldwide, only a few languages have affricates in these positions, even though the corresponding stop consonants are virtually universal.
Note that a fricative is a single speech segment, not a sequence of two sounds. In some languages (e.g. Polish) affricate and "stop plus fricative" clusters contrast very clearly, as in czysta 'clean (f.)' [tS...] versus trzysta 'three hundred' [t|S...] (the vertical line separates segments). In English the cluster [ts] occurs, as in bats, but it doesn't function as an affricate.
For special types of affricates, see also: clicks