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He has a prior engagement this evening.

Now what does it mean? Does it mean his engagement is going to happen before someone else or at first please explain.

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It is implied that he has been asked/invited to do something this evening, but he already has an earlier, or "prior", engagement, so he cannot accept.

Comments  
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Ok does this engagement mean that he's going to marry?
Liton Das Ok does this engagement mean that he's going to marry?

No, it isn't that kind of engagement. It means an arrangement or appointment to do something (e.g. attend a party, visit someone, etc.).

Oh thanks and I've been thinking that engagement means pre married procedure for all my life.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Liton DasOh thanks and I've been thinking that engagement means pre married procedure for all my life.

It can mean that, but not always.