Hi Deisy,
“Remind” basically means to prompt someone about something else. In other words, when you remind someone of something, you bring something (a memory, a word, an event, etc.) to the attention of someone.
“Remember” is when you recall or recollect something such as a past action or event.
The two concepts are closely related -- and I’m not sure I’ve made that very clear. Hopefully, someone will be able to add better clarity than I have!
In addition to the excellent answers that are already here, I thought I'd offer a couple of Spanish sentences which illustrate the difference:
Le recuerdo que tengo un compromiso antiguo a este respeto. = I remind you that I have a longstanding commitment in this area.
Remember is when you think of a memory (a past experience) and Remind is when a person or thing makes you think about something.