A Slayer tome is a experience reward from the minigame, Temple Trekking. You can get one by taking one of the followers to Paterdomus or to Burgh de Rott. At the end, you will get a Reward token which you can exchange by clicking on the first option, Claim-reward. The Slayer tome grants Slayer experience once read. The colour of the tome depends upon the level of the reward token. A higher level reward token will give more Slayer experience.