Wikipedia only yields a cursory overview of the events leading the Velvet Revolution, but it doesn't really give an idea of what day to day political life was like for the average person. How accessible was party politics? Why couldn't the people simply vote in new delegates and reform it?
There certainly was a political life in communist Czechoslovakia, but not in any shape or form close to what we understand as politics today, with the connotations of political pluralism, opposition, different candidates nominated by their parties competing for voters in free and transparent elections. While elections did take place, people could not "simply vote in new delegates and reform it" because the selection of these was dictated by the regime, and the voters did not actually get to choose.
It is true that there were other political parties than the Communist Party of Czechoslovakia, but they were nothing but puppets united in something called the National Front. What started as a still somewhat varied and at least partially democratic national unity government of sorts after the war turned into a monolithic block after the 1948 coup. Whatever political parties (or even groups such as unions or youth organizations) remained in it underwent purges and reforms, and the National Front became nothing but a front for an entity completely controlled by the communists.
During elections, the voters did not get to choose from several candidates representing various parties as is the norm today. Rather the National Front decided on a list of candidates, and the people simply confirmed these with their votes – or not, in theory.
While strictly speaking voting was not mandated by legislation, people were forced into accepting these candidates and faced persecution had they abstained from voting. Official statistics show turnouts of over 99 percent being the norm, with blank votes in the hundreds or low thousands making up an absolutely negligible percentage of the votes.
Even the Prague Spring, a period of liberalization in the 1968 that followed the general trend of destalinization in the eastern bloc, was by no means an aggressive reform of the above, nor an attempt at escaping the Soviet sphere of influence and aligning with the West. Instead, it was a fairly mild process of minor decentralization still firmly rooted in socalist principles with the communists at the helm of the country and its politics.
It all boils down to the fact that the political scene was dominated by the ruling party. Even though elections were held, they existed in a strictly communist controlled framework. While a non-communist candidate could be elected, he would still be a part of the National Front. There was no external opposition that could take part in Czechoslovak politics, and what differences might have existed would be internal to the communist controlled politics of the time, preventing any potential significant reform.