So, your textbook sounds a little bit useless! This might be because it's poorly written, but I think it also reflects how difficult a figure like Franco is to understand or describe. Franco was not a Hitler or even a Mussolini - he was not driven by his beliefs to do awful things. Rather, Franco's beliefs tended to reflect his own needs. In other words, he was often willing to change his policies depending on what looked like keeping him in power longer. He was in many ways traditionally conservative – he wanted Spanish society that returned to older values: Catholic, pro-Army, paternalistic and anti-modern. So while Franco’s support was always coming from the conservative elements of society that shared similar values, how these values translated into action depended on the internal and external political situation.

Most famously, this was reflected in the people he chose to be in his government. Franco’s power was always based on a broad coalition of right-wing elements, and he could use his position to adjust which of these groups were given power in the new state. In the first years of the Second World War, when Germany seemed to be winning, Franco filled his government with fascists and other German sympathisers. But when the Allies started winning, he got rid of many of those people and replaced them with individuals he thought the Allies would see more sympathetically. After the Second World War, he focused on his Catholic and anti-communist beliefs to appear more sympathetic internationally, particularly to the United States. So, despite leading a regime that was brutal and repressive, and had helped Germany for much of the Second World War, Franco managed to survive and even become a US ally later on.

So where does this leave the two specific claims made in your textbook? The first, that Franco wanted an equal country, seems very wrong. Franco’s main concern was always maintaining his power. Internally, this meant rewarding his various supporters (but not too much, so they didn’t get powerful enough to overthrow him), often at the expense of his internal enemies, particularly those who had been on the other side of the civil war. If you had fought for Franco’s army in 1936-9, for instance, you got a pension and higher social standing, but veterans of the Republican Army got nothing, even if they had been wounded and couldn’t work. In this sense, Francoist society was purposefully hierarchical rather than equal. I think what the textbook was trying to say though was that Franco was influenced by corporatism. This is a way of organising society that is closely associated with Catholicism in the period as a counter to socialism – that instead of competing, different classes should work together as part of the nation. In theory, this means that different segments of society – workers, business owners and so on – would all get a say in how decisions were made, so that policy represented everyone’s interests. In theory, this is supposed to lead to a more equal, harmonious society. But in reality – and here is where the second point about favouring the rich comes in – corporatist systems tend to work best for those close to the government. In this case, because Franco relied on the political support of Spain’s wealthier classes – industrialists and landowners, for instance – their needs were better looked after than many poorer people. Moreover, because most of Spain’s trade unions and workers’ political parties had been banned by Franco, there was no way for their views to be properly represented in any case.

I have tried to keep my explanation and language simple, as you requested – there are naturally complications and details I have skipped over. Please let me know if you would like me to go into any more depth anywhere!