Here's a breakdown:
* お会い (oai): Meeting (honorific form)
* でき (deki): To be able to, to manage
* て (te): A grammatical particle connecting verbs
* 嬉しい (ureshii): Happy, glad
* です (desu): A polite sentence ending
This phrase expresses your happiness at meeting someone. It's a very polite and formal way to say it.