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Can someone explain what reaction is going on here? I looked in my list of mechanisms learnt: I find nothing related!

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    $\begingroup$ If you've learned the E1 reaction, this is the reverse process, as detailed by Jannis below. $\endgroup$ – jerepierre Sep 6 '14 at 15:53
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It is an acid-catalyzed hydration of the double bond. First, the double bond is protonated to yield the tert-butyl cation which is most stabilized by hyperconjugation (protonation at C2 would form a less stable primary cation). The cation is captured by nucleophilic attack of water, which after deprotonation yields tert-butanol and the regenerated proton.

$$\ce{(H3C)2C=CH2 + H3O+ <=> (H3C)3C+ + H2O} \tag 1$$

$$\ce{(H3C)3C+ + H2O <=> (H3C)3C-OH2^{+}} \tag 2$$

$$\ce{(H3C)3C-OH2^{+} + H2O ->~ (H3C)3C-OH + H3O+} \tag 3$$

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