A hard fork is an expansion of the rule-set, meaning that previously invalid blocks become valid according to the new rules. In regards of software you can also call it a backward-compatible update.
Soft-forks are compression of the rule-set, so the new rules still conform to the old rules. This can only be possible by stricter rules (reduced possibilities). What was previously allowed is not allowed any more. Who ever follows the new rules also automatically follows the old rules. For the blockchain this means that previous valid blocks become now invalid (according to the new rules).
In general a hard-fork reduces restrictions leading to new or more possibilities. The side-effect of this is that more possibilities lead to increased complexity and reduces security. If you are somehow in software development you know that there are principles that programmers follow to increase security, maintainability and reduce dependencies. A favorite example are the SOLID principles, which are just restrictions.
One of the reasons for a hard-fork can be that there is no consensus in the changes. One way to handle this situation is to agree that you do not agree and each party continue following their own rules. You can also call this diversification.
For the blockchain itself it means a reduction of power. The power (here hash-rate) is split up, leading to weaker network security. There is deconcentration of power for the complete network but a concentration of power in single spots or parties/groups. The ones that had more power now become more powerfull. More power on specific spots may lead to missuse of that power. So it becomes easier for those who want to cheat that have more power and weakens the ones that have less power.