This may be an interesting subject in the current political climate but let's try and understand what democracy actually is. When humans gather together to make collective decisions, they must be made either in a democracy (Greek dēmokratía), 'rule by people'; or by an aristocracy (aristokratía) 'rule by elites. Within each idea are numerous types, subdivisions and systems that help a society make good decisions in a timely manner. All societies struggle with the perfect system for their circumstances. Aristocracy would, on the face of it, seem like a good system; who would not want complex and difficult decisions made by those best trained and experienced to deal with them? However this system leads to abuse by those selected when they can make decisions that benefit themselves and their families to the detriment of non-voters. It also tends toward monarchy (rule held by a single person) and hereditary monarchy (rule by a family). For the ancient Greeks, democratic decisions made within an aristocracy was the best form of government as long as hereditary succession was outlawed. Those same ancient Greeks believed that the issue with true democracy was that it tended to mob-rule. If the uneducated and ignorant can make decisions then they would make uneducated and ignorant choices. The assumption was that the masses could only produce average policy, while the best of men (and it was men only) could produce the best policy, if they were indeed the best of men.
As society has evolved and changed over the centuries since, monarchies have given way to aristocracies which in turn have given way to democracies. Democracy has taken a number of forms, both in theory and practice but there are many different varieties, all with benefits and challenges. Direct democracy is where citizens themselves make decisions that the executive carry out. Usually this involves a referendum or a series of votes on issues. Switzerland is a good example but even though its citizens vote four times a year on various questions, there is still an executive that has a say in how the instructions are carried out. Two Swiss cantons have a pure form of direct democracy and all citizens have a regular vote on all decisions (though one of these only gave women the vote in 1991). Most democratic countries are 'representative democracies' or a hybrid of this, direct and aristocracies. The people in these countries elect representatives to make decisions on their behalf. If the head of the state is elected then it is a Republic. All systems have to have a series of checks and balances in order to minimize the abuse and tendency to mob rule in democracies or hereditary succession in aristocracies. Most countries have settled on hybrids that try to benefit from the advantages of both systems and it is the tension between the two that causes many political arguments.
In the UK we have a hybrid democracy. We elect our MP's to represent our will in a parliament and they in turn select a government or executive to manage the day to day decisions. Though ultimately the monarch is the head of state (in the form of the King or Queen) and parliament acts at her discretion, the power of the monarch has been reduced so that its power is paid lip-service to by parliament. We do not have a direct democracy. Our 'Will' comes from the election of representatives at various levels - local, regional and national - to manage and make decisions on our behalf. No system can please everyone or act in everyone's wishes and we must ensure that whatever system we use, robust checks and balances are in place to ensure abuses are contained.