It certainly doesn't mean electricity! The truth is, we don't really know what it means. And whatever it is, studying it is dangerous! Some of you may recall the story in BT Hagiga 13a, where a child is studying Ezekiel, ponders over the meaning of hashmal, and was consumed by fire. You have been warned...
From the context, it appears to be some kind of shining substance. Elsewhere in the pereq we see ke'ein nehoshet, "like [the colour] of copper", and in Ezek. 8:2 hashmal is connected to zohar, brightness of some sort. According to Gesenius, hashmal refers to polished bronze: the etymology being [n.]h.sh., "copper or bronze" (like nehoshet) + m.l., "to soften or polish". Contemporary scholarship (e.g. Brettler's commentary in the Jewish Study Bible, and Bodi's work here) seems to argue that it is more likely to be derived from an Akkadian word which is ambiguous in referring both to the substance of amber and to some kind of shining metal.
Now, the Septuagint translates hashmal as elektron, which (like the Akkadian mentioned above) has two meanings in Greek: a shiny, bronze-coloured metal alloy made from gold and silver (also known as electrum in Latin), and amber, which has the same colour. (By the way, elektron as amber is the root of the word electricity, since the first experiments with electric properties were done with static electricity produced by rubbing pieces of amber. The Hebrew poet Yehuda Leb Gordon therefore proposed the word hashmal to mean electricity in the late 1800s, which meaning it still has in Modern Hebrew today).
There are certainly differing interpretations: in Hagiga 13b the rabbis understand it as a notarikon/ acronym for hayyot esh memallelot, "speaking Beings of fire", (and thus Rambam puts Hashmallim as the fourth level of angelic being in his classification in Yesodei haTorah 2:7), and other rabbis and mepharshim give other explanations, as the other answers to this question show. But at least on the peshat level, I would say that hashmal appears to refer to a warm shining color, similar to amber and/or a metal like bronze or electrum.
Edit: Edward Greenstein's work in Holtz's "Back to the Sources" directed me to the beautiful commentary of Rabbi Eliezer of Beaugency, a 12th century French exegete, who writes on the hashmal:
כעין החשמל: בדבר הנראה לנו הנביא מדמה, כענין תרשיש, כמראה הלפידים, כעין הקרח הנורא, כמראה הבזק, כעין נחשת קלל, כמראה הקשת. כלם בנראה לעולם, אף כעין החשמל דבר הוא בעולם, אבל אין אנו בקיאין בלשון המקרא ברוב דברים ואין לנו אלא הענין. וענינו יורה עליו כי זוהר צח וברור במאד מאד הוא כזוהר ברירות החמה שנראית נעה ונדה כגלי מים.
Ke'ein hahashmal: the prophet [Ezekiel] uses comparisons to things visible in the world, such as "the [stones of] Tarshish", "like the appearance of torches", "like the colour of the dreadful ice", "like the appearance of a lightning bolt", "like the colour of burnished copper", "like the appearance of a rainbow". All these things are visible in the world, and so "like the colour of hashmal" [must be] something in the world; however, we are not proficient in the language of Scripture in many things and we have nothing but the context [to go by]. The context here indicates that [hashmal] is a very, very clear and bright radiance, like the radiance of the brightness of the sun, which appears to ebb and flow, like waves of water.
I love this, both for his prescience in understanding hashmal as a shining bright colour, and for his honesty in acknowledging that when it comes to Biblical language, we often simply do not know what precisely it is referring to.