Laud's reform of church ceremony and religious architecture had many aspects which were aimed at creating a more centralised, unified and hierarchical church organisation in the Church of England. One aspect of this, although some have argued that this originated with Charles I rather than Laud, was the movement of communion tables from the centre of the church to the east, that they be covered by rich decoration and candlesticks and enclosed by rails.
So, why was this minor change cause such a massive fuss? To put it frankly, the whole thing stank of "popery." First of all, reformed churches, which the Church of England technically was, did not have altars but rather communion tables. This is because you perform sacrifices on altars and the reformed did not believe in the literal transubstantiation of the bread and wine into the blood and body of Christ. Instead they viewed it as a symbol -- no miracle took place. If there was no miracle, therefore no sacrifice and therefore no need for an altar. So that was the technical theological reason.
However, that doesn't account for the rage over altars. That was because the entire thing was a symbolic struggle over the direction of the Church. Laud represented the Conservative faction around the king. The former, at least, was an Arminian who believed to a certain extent in free will and as noted before wanted a more authoritarian and centralised church. The Puritans, by contrast, wanted a more decentralised church which stressed Calvinist predestination. They also feared a slippery slope. Any backsliding on reform, in their view, was not only sinful but it might presage s return to devilish popery. Such fears were only magnified by the known Catholic sympathies of Charles and the Catholic clique surrounding his French wife Henrietta Maria of France.
As such the arguments over the altars, the content of the book of common prayer, episcopal vs presbyterian government and so on which raged during this period were all parts of a broader conflict: which direction would the church go? Would it emulate the stern reforming zeal of Geneva based around small independent churches or a more moderate - some would suggest "Crypto-Catholic" route.