Polonium
Here is a Wikipedia description of the element. As noted there, it is an alpha particle emitter. Follow the link to the ”Alpha Decay” entry and you find out why this stuff makes a good poison.
Alpha emissions are stopped by most materials. Glass will protect someone. Even the thin layer of dead skin on the surface our bodies will do the trick. Unfortunately, alpha particles play havoc with living tissue. Thus a would-be poisoner could carry the material in relative safety. The tricky moment would be depositing the material in such a way that it would be either ingested or inhaled by the victim alone.
As this Guardian article notes, the use of such a poison raises disconcerting questions concerning the availability of nuclear materials for undercover and terrorist actions. Polonium is rare. Most of it is manufactured or “transmuted” by bombarding bismuth with neutrons. (See this article from GlobalSecurity.org for a brief history of Polonium, including a discussion of its use in weapons.) As the Guardian article notes, this is not the weapon of a lone assassin.
It is also a strange poison to use, if you think about it. It is hardly a covert weapon. In fact, its use practically screams “look what I did” to the wider world. If this was Putin’s idea, as Litvinenko himself thought, it is intended to scare all expatriate critics, at least all with inside information. If it is his idea, it is also a very direct and worrisome message to other governments about the lengths that his regime will go to in suppressing any form of threat.
Of course, if Putin did not order it, that’s even scarier. It would suggest a serious new leak in the security surrounding Russia's nuclear assets.