A Slayer tome is an 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 can be exchanged by clicking on the first option, Claim-reward. The Slayer tome grants Slayer experience when read. The colour of the tome depends upon the level of the reward token. A higher level reward token will give more Slayer experience.
||Random amount of Slayer experience. (1100-1650)
||Random amount of Slayer experience. (2035-3025)
||Random amount of Slayer experience. (4015-5005)
For an exhaustive list of all known sources for this item, see here