Some particularly powerful Creeps will seek to take out your Towers with powerful attacks. If a Tower is damaged it will not lose effectiveness but it is at risk of being destroyed by subsequent hits. Once a Tower is destroyed its Elixir cannot be salvaged but the Plot can be used again.
If a Tower is only partially damaged you can choose to Repair it with Elixir by tapping on it and selecting the Repair Button. A Tower will always attempt to repair to full health or as close as it can get with the Elixir you have available to you.