Why can covalent compounds conduct electricity?
Generally speaking, they do not - though there are exceptions.
In order for compounds to conduct electricity, there must be charged particles present - such as the case with ionic compounds which are composed of positively or negatively charged ions. There are also scenarios where unpaired electrons can also be free to conduct charge.
Acids, for example, can ionize in solution to produce ions, which are free to conduct electric current.
Certain polymers, with free electrons or multiple bonds can also conduct electric current.
Graphite also has a free electron which allows it to conduct electricity, even though it is composed of several covalent bonds.
So typically, even though we think of ionic compounds or metallic compounds able to conduct electric current, there are some instances where covalently bonded molecular compounds can conduct electricity as well.