Answer:
A free and fair election basically means that the election is free from coercion. Voters must be free to choose their candidates without fear of persecution either from the state or other citizens. Parties must be able to nominate themselves for government without fear of persecution and violence from the current government, military or from opposition parties. The counting of the votes must also be transparent and independent to ensure that the election votes are not tampered with.
Basically, to ensure they are free and fair you need someone who will make them so, regardless of any bribes or threat attempts against their person. If you can't guarantee they are fair via a transparent process (keeping records of who did what, allowing impartial inspectors to oversee certain parts of the process, etc.) then nobody can trust the results; if you can't guarantee freedom of choice then there is no point in having an election and it is therefore not democratic.
The challenges, however, are revealed by differences in liberal democracies. The USA does not have a compulsory voting system, which means many American citizens do not register to vote. Some of the reasons given for this is that voting is difficult or inaccessible (difficult to access polling booths, voting times coincide with work times, etc.). So from this perspective it is not free and fair since the voting system itself must be easily accessible for the population.
In some nation-states, there is no cap on election campaign spending. In this sense, parties that can amass wealth are able to afford better and more pervasive election campaigns. Again, this questions whether elections are free and fair since political parties that are funded by the wealth of high-earning populations have an unfair advantage.