[出会]{であ}えてよかった。
translates to "A was happy to have been able to meet B" or more literally "it was good to have been able to meet B."
(just from the fragment I'm not sure who A and B are).
Now, I'll give explanation a shot. You're completely right that is a form of the verb [出会]{であ}う.
As a Go-dan う verb, the potential form is 出会える.
出会えて is a conjugation often called 〜て形 in foreign language learner contexts (I learned it that way a long time ago).
In this case, this て case ending means "because"
You state:
Well, obviously verb can not be the front of sentence (in Jp)
I think I get what's motivating this sentence, but it is at best ill-worded.
What is closer to being true is that in a Japanese sentence, the main verb of the sentence comes at the end of the sentence (though there can be sentences with no verbs ones where there's no verb in that position) in contrast to the preference in English and Chinese for the verb to be in the middle.
Words that are verbs or their conjugations can occur just about anywhere in a sentence in Japanese. (This is I think less true in English).
In the sentence you give, よかった function as the verb. The かった end marks it as the past tense form of an adjective -- specifically the adjective よい (いい）...
