If you grew a pepper plant in isolation, so that it fertilized itself, then the seeds produced will grow into similar plants. However, despite being self fertile, peppers can be fertilized by another, separate pepper plant - when that happens, you don't know what you're going to get when you grow from any seeds produced.
Added to that, F1 hybrids are obviously all the same - but the F2 generation (which would be the one you grow from any seeds you save) may not be, even if they are not fertilized by any other pepper - there will be some variation because of recessive genes. There is an advantage in this - its the reason there are so many, and still increasing, varieties of pepper, but in terms of being sure what you'll get from your saved seed, it's a disadvantage if you want exactly what you got the first year.
Work continues by seed producers though - in some places, there are on sale F1, F2 and F3 seed varieties of Trinidad hot peppers, results of continual crossing by growers, but growing from seed you've saved yourself does not produce guaranteed results, though it might make an interesting experiment.