The majority of the time, most typical clients won't be saturating your internet bandwidth.
Now, let's say you have four clients and two are idle, while the other two are downloading a large file. You don't want each to be allocated a maximum 25% of bandwidth, because that would mean that there is bandwidth that is going unused. You probably, instead, want the two that are downloading a large file to each get 50% of the bandwidth, but for that to drop if one of the idle clients suddenly starts utilising the connection. Now, as long as this is the behaviour you want, you don't have to do anything to achieve this; internet routers will do this anyway given other factors (number of connections open per client, buffers, etc) are equal.
Now, let's say that you have four clients and two are idle, one is downloading a large file using a single TCP connection, and another is downloading using 50 TCP connections (which may be the case if they're using a peer to peer service, for example). You don't want the person using 50 connections to be getting 50x the bandwidth as the person using one connection. Without any kind of shaping, this is what would happen under most internet routers.
QoS is an umbrella term for a variety of different ways of shaping traffic through a router. Note that you will only have control over the outgoing bandwidth from your clients, not incoming - that would need to be shaped on your ISP's side to be effective.
With QoS you can give some types of traffic, such as HTTP traffic, priority over other types of traffic. Or, you can give each client a minimum guaranteed bandwidth that, if they need it, they can have it (but if they're not using it, others can still use it). This is probably the way to go, IF your router does support that type of QoS control (which not all do).
Since you can only shape the outgoing bandwidth, this will have limited effect, but it can still have an influence on incoming bandwidth - every incoming data connection relies on periodic feedback from the receiving end that they are receiving the data.