It means that he must follow the law without favouring anyone. For example if he saw a robber breaking into a shop and he arrested him, the policeman musn't then let him go if the robber said he was really really sorry.
'Disinterestedly' implies that an officer must not be interested in what he is doing, but it actually means that he must not have an active interest in enforcing - or not - the law. For example - he mst not refuse to arrest a friend or aqauintence, he must remain impartial - enforcing the law equally and fairly, in a balanced way.
"Disinterestedly" doesn't sound right: shouldn't it be "dispassionately"?
Police Officers are told that they must apply the law "without fear or favour", in other words, you'd better be prepared to arrest your own granny if necessary!
If that doesn't give you an idea of the definition, nothing will!
disinterested and impartial are pretty much the same thing: it means not taking sides, not treating one person differently from another. I'm not sure why both words are used.
(Disinterested isn't the same as uninterested, by the way.)