Pragmatically, May it please the court is an archaic formula expressing the speaker's deference to a presiding judge: an acknowledgment that strictly speaking nothing may occur (and nothing may be omitted) in the courtroom without the judge's permission.
The syntax—the part of the meaning which is expressed by the order and relationship of different words—is complex.
In this particular forumula, please is an ordinary transitive verb. It (which refers to the main clause which follows) is its subject and the Court is its object. Please itself is cast in the infinitive (non-tensed, non-inflected) form because it is the complement of the modal auxiliary verb may, which is the finite head verb of this clause.
Internally, the inversion of may with its subject (may it instead of it may) signals that may bears an optative∗ sense—it expresses a wish or hope.
May you be forgiven! = I hope that you will be forgiven.
May God strike me dead if I am lying = I hope that God will strike me dead
May it please the Court = I hope that it will please the Court.
Such optative clauses may stand on their own as independent clauses, as they do in my first two examples. In this case, however . . .
Externally, the formula acts like a condition clause (an if clause or protasis) in a conditional construction of the sort that Declerk and Reed† call a ‘Performative-Q Utterance conditional’. In fact, it can also be expressed as a frank if clause: If it please the Court.
It expresses a necessary condition for the following consequence clause; it is semantically equivalent to
I only say what follows if it pleases the Court that I do so.
The expression is entirely archaic, used nowhere except in the courts and by nobody except lawyers; I can think of no other situation in which such extreme deference is called for. (It may be that formal addresses to the Queen are prefaced with ‘May it please your Majesty’, but that is not a situation likely to arise for most of us.) It should not be emulated in ordinary speech or writing. In most contexts the Present-day English equivalent is a simple Please:
I would like to speak with you, please.
Please, I would like to speak with you.
In these, please is no longer understood by native speakers to be any sort of verb; it is merely a "discourse marker" expressing politeness in making a request.
∗ Optative is a technical term signifying a particular modality which marks a sentence as having some meaning distinct from an ordinary assertion of fact. Linguists have had to name many such modalities, because every language has different ways of expressing different shades of meaning.
Some languages use distinct inflections of the verb to express particular modalities--for instance, the subjunctive inflections in many European languages may express modality, among many other things.
In other cases modality may be expressed by particular words; in English, for instance, possibly (epistemic modality), wish or hope(optative modality), let's (modality), and so forth.
English also has a very small number of verbs (can/could, may/might, must, shall/should, will/would) with distinct syntactic properties which are called modal verbs because they are ordinarily used only to express modality. Unhappily, they are called upon to express many different sorts of modality, so it is very difficult to learn how to use them properly.
† Conditionals:A Comprehensive Empirical Analysis, Mouton de Gruyter 2001.