A kit lens can be very good for everyday shooting, and for small prints or screen viewing there may be little reason to upgrade. The main limitations versus a better standard zoom are:

• slower maximum aperture: kit lenses are often around f/3.5-5.6, while higher-end zooms may offer f/2.8. This helps a lot in low light, allows lower ISO, and gives shallower depth of field for portraits.
• optical compromises: you may see more chromatic aberration/fringing, and sometimes less contrast or color rendition, especially when viewed large or closely.
• build and handling: kit lenses are usually lighter and less robust, with basic manual focus rings and less refined operation.
• autofocus and focus feel: autofocus may be slower, and manual focus control is often limited.
• rotating front element: this makes using a polarizing filter inconvenient because focus changes can rotate the filter.

In short, if the lens is meeting your needs, keep using it. Upgrade when a specific limitation starts to matter to you—most commonly low-light performance, background blur, filter use, or wanting better performance for larger prints.