Short answer: A hard fork means you have to update your client software. If you use an online service, they have the responsibility to take care of it.
Medium answer (technically correct which means possibly wrong): A hard fork means the consensus protocol is updated in a backward incompatible way, say increase block size from 1MB to 2MB. Existing software will not recognize new blocks or transaction data (because they are not compatible). Therefore, new data will be rejected. If some miners still run old software, they will produce blocks in the old format and other users will accept that instead. This split the community into 2 groups: one that follows the old format and another that follows the new format. Thus, the perceived "chain" is split into two while technically, each group still only see one chain.
Long answer (technically irrelevant and possibly correct): Because software are never perfect, there are times you have to update. Sometimes it is to fix bugs, sometimes it is to add new features. Bitcoin Cash does it twice a year (think major Windows update or major Android/iOS version). These are usually considered "non-contentious hard fork" because pretty much everyone (developers, users, hodlers) agrees that the changes are good and no one bothers running old versions.
However, the upcoming hardfork is a contentious one. Without getting into technical details, it is similar to changing traffic law to make everyone drive on the right instead of on the left side of the road. There are supporters and detractors on both sides. While there are good arguments about human physiology (more people are right-handed) or availability of cars or following popular conventions like the rest of the world, contentious hard forks are usually a split in ideology. In the cryptocurrency space, without a central authority, everyone is free to follow what they like to do. As a result, cars will crash into each other (the equivalence in cryptocurrency would be losing coins). Thus, most exchanges usually decide to stop everyone from driving (withdrawal/deposit) until the dust has settled and there is a clear winner. In the case where there is no clear winner (as shown through the BCH vs BTC split), they would build extra roads (one for left side people and another for right side people) and let people drive with their own set of rules on those roads. It may sound silly but such is the implication of decentralization.