Dead-heading a flowering plant means to remove faded flowers. The purpose of doing this is to stimulate the earliest possible development of new, young shoots and further blooms throughout the flowering season. On roses, once a rose flower has been fertilized it will soon fade and if left on the plant it may delay the production of new shoots below the old flower cluster.
In some roses, a hip or a seed pod will form after the flower is fertilized and this diverts energy from further flower production. If you don’t need the hips for ornamental purpose then you should remove the dead flowers regularly to keep the rose flowering throughout the summer.
In autumn, even if some of your roses will continue to bloom, do not dead-head them anymore to avoid encouraging new, soft growth which would be damaged by the first frosts. Let the flowers on the plant until the autumn cut-back.
Different types of roses need different methods of dead-heading. On Floribunda Roses, the central bloom of a truss will fade first and should be cut out to maintain the display. Then, when all the flowers have faded, remove the whole truss by cutting back to an emerging bud or a fully formed shoot. On Hybrid Tea Roses cut back stems bearing faded flowers to an outward-facing bud or fully formed shoot.
Also you might find on your roses some blind shoots. These are shoots that develop without a terminal flower bud. They divert plant’s energy just like a sucker. Prune them out as soon as they appear. Cut the blind shoot by about a half to an outward-facing bud to encourage it to grow away and flower. If no but is visible then cut back the whole shoot to the main stem.