usage - 〜くて form of a verb

I ask here my question because I couldn't find anything on internet. My problem is about 〜くて form for a verb.

I asked a Japanese friend what for example "会いたくて" means. She told me that there is a complicated nuance behind that... It means

I want to meet you (but I can't)

I didn't have the opportunity to ask again so I ask here. Could someone explain to me the usage of 〜くて? I'm so confused (>_<). Especially with the form which expresses the desire like "食べたい" → "食べたくて".