If a card appears on the banned list for your chosen format, then you may not include that card in your deck or sideboard. Doing so makes your deck illegal to play in any sanctioned tournaments for that format.
Cards are usually banned from play if they enable a deck or play style that heavily skews the play environment. What does that mean? If the card were legal, a competitive player either must be playing it, or must be specifically targeting it with his or her own strategies.
Some cards are banned because they have proven to simply be too powerful in their respective format. While hundreds of hours are spent rigorously playtesting sets before their release, the complexity of Magic makes it nearly impossible to accurately predict all the ways the new cards interact with older ones.
If you wish to use a card that’s on the restricted list for your chosen format, you may include only a single copy of that card, counting both your main deck and your sideboard. Currently, only the Vintage format uses a restricted list.