Equivalent Series Inductance or ESL is an inductance value representing the distributed inductances associated with a real capacitor (as opposed to an ideal capacitor). Real capacitors do not merely have a capacitance associated with them but also an inductance and resistance (See ESR). ESL is not normally a consideration at low frequency operation but becomes more important at higher frequencies. Certain types of capacitors such as ceramic disk capacitors have a low ESL whereas aluminum electrolytic capacitors have a rather large ESL. Capacitors with a high ESL are usually reserved for low frequency power supply filtering. It is hard to calculate a value for ESL and therefore manufacturers usually do not have numbers available.

The equivalent circuit for a capacitor can be represented by the schematic in figure 1. This is not entirely accurate but is a good approximation at low frequencies.

              ESR      ESL       | |
        -----/\/\/\---UUUUU------| |------
                                 | |

        Figure 1: Schematic representation of a real capacitor

Straw, R.D. Ed. The ARRL Handbook for Radio Amateurs. Newington, CT: ARRL, 1999

Thanks to JerboaKolinowski for the hard link from ESL and for the suggestion that I explain why the acronym for "Equivalent Series Inductance" is ESL and not ESI. It just so happens that the letter "I" is already used by electrical engineers to represent an electrical current. You may ask why they did not use "c" to represent an electrical current. Well, because that letter is used to represent a capacitance silly. Why they chose "L" as a representation of inductance is unknown to me, but it is pretty universal.