The emails are from crooks trying to steal your money or your identity.
Con artists claim to represent former government officials in Nigeria or another country and ask for your help to transfer large sums of money out of the country because they know you are "honorable". If you respond, they ask you to send money, using plausible sounding excuses like transaction costs and attorney's fees, or ask for your bank account numbers or other identity information. They may even encourage you to travel to complete the transaction.
The best thing to do is to not reply to any emails that seem suspicious. If you receive such an email, report it to the abuse department of the domain used by the scammer. You can often obtain the email address of the abuse department by changing the left hand side of the scam email address to the word abuse. For example, if the mail originates from email@example.com then write to firstname.lastname@example.org, etc.
Visit the Interpol Web site on Information Technology Crime to find more prevention techniques, and the latest efforts to fight this kind of crime in the EU. More information on enforcement of laws regarding email scams can also be found on the Web site for the Regulation on Consumer Protection Cooperation (CPC), developed by the EU. See, What are email scams?