An infix is a simple affix that is inserted into a morpheme (cf. Helmbrecht & Lehmann 2008, section 3). Here is a stock example from Latin conjugation (the present is formed by infixation):

a.scid-i
Lattear- PRF.1.SG
I tore
 b.sci<n>d-o
 tear<PRS>-1.SG
I tear

The above definition requires the following comments:

Diachronically, an infix can originate in two ways, either by metathesis or by entrapment.

In 99% percent of the cases, the host morpheme of the infix is a root. However, by entrapment, it is even possible to get an infix into an affix. Here is an example from Gedeo (Highland East Cushitic), from Gragg 2008:

Negation in Gedeo
polarity
person   ╲
affirmative
meaning
negative
1 sghaʔw-aannoI drinkhaʔw-a<bo>ʔno
2 sghaʔw-tattoyou drinkhaʔw-ta<bo>tto

What appear synchronically to be monomorphemic 1st and 2nd singular suffixes were originally composed of two morphemes, the first marking person and the second marking aspect. The negative suffix attached to the first of these, and then followed the aspect suffix. Later the person and aspect complex was monomorphemicized so that the negative suffix got entrapped and became an infix.


References

Buccellati, Giorgio 1997, "Akkadian." Hetzron, Robert (ed.), The Semitic languages. London: Routledge (Routledge Language Family Descriptions); 69-99.

Gragg, Gene 2008, "Morphological expression of verbal negation in Cushitic". 3rd Meeting of the International Association of Comparative Semitics, Turin, 2 - 5 october 2008.

Helmbrecht, Johannes & Lehmann, Christian 2008, "Hocank's challenge to morphological theory." Harrison, David & Rood, David & Dwyer, Arienne (eds.), Lessons from documented endangered languages. Amsterdam & Philadelphia: J. Benjamins (Typological Studies in Language, 78); 271-315. [ download PDF ]