Warrants may be issued as an inducement to buy a stock or bond issue. I don't think they are as popular today as they were 20 or 30 years ago (don't know - haven't been in that market for 20 or 30 years).
A warrant gives one the right to buy a common share at a set price up until a set time. e.g. Yamana Gold C warrants allow you to buy the common share at $6 until (sometime, not sure when, in) 2010.
If the share trading price is below the warrant exercise price, the warrant is worthless, but it would typically trade for a few cents. Also, the warrant is worthless after the expiry time. It is the scenario in between where it gets interesting. It is all about leverage.
Yamana Gold is trading about $8 now. The warrant is about $1, although you would think its 'value' shouls be $2. Go figure the market. If Yamana Gold were to double to $16, then the warrant would be 'worth' $16-$6 = $10. So, your leverage (taking the actual market price) would be about 10/1, which is terrific. There is lots of time left on this warrant, which is good. Typically, the lower the leverage, the less desirable the warrant. Exercise price and expiry date are what are important.
I recall than Morton Shulman (Ontario Chief Coroner in the 60s or so) wrote a book "Anyone Can Make a Million, and he had a chapter devoted to warrants.
Hope this helps.