It’s not a stupid question! Gardening is complicated when you’re just getting started.
The good news is that no, you don’t have to remove plants after one season to replace them with others (in fact you really shouldn’t do that). Hardy perennials (which is what you would plant in your border) live for many years - peonies for instance can live 70 years or more, coming back every spring.
The advice you are being given is to have a mix of plants that will look their best in different seasons, so your border is interesting all year round. So you would have plants that bloom in early spring, late spring, summer, autumn, winter etc. When they are done flowering, they will sit there happily, providing a backdrop in structure and foliage for your other plants. They will also get bigger every year, so your border will look fuller.
The bad news is that even if you restrict yourself to hardy perennials, there are still thousands of choices, and it can get a bit overwhelming.
Oh and once your perennials have gone in, in the autumn you can put lots of bulbs (tulips, daffodils, alliums) in the ground in all the gaps, to flower the next spring.
You can also fill gaps with annuals. These are plants that are not hardy, so will die after the first frost. These are the plants that are sold in little six-packs in supermarkets and garden centres, like begonias, impatiens and petunias. They give instant gratification as they start flowering straightaway. However, they only last a year.