It’s very simple,
A hard fork is a change in the block or blockchain format, that requires a change of the wallet and sometimes of the miner software also.

It’s called hard fork, because older clients can not process Blocks created after the fork.
The danger is, that if a high number of clients and miners stay on the old software revision, there may be two branches of the blockchain, that can’t convert anymore.

If comparison a soft fork is a change in the blockchain protocol, that does not have this risk.