Google Translate tells me the meaning is 'get away with me' and some other dictionaries also give me answers like 'escape me' or 'come away with me' or something like that.
Could anybody offer a simple explanation for it?
Instead of using robots to translate and online dictionaries, try using the DRAE (diccionario de la Real Academia Española).
"Conmigo" means "with me". From the dictionary
conmigo Del lat. cum 'con' y mecum 'conmigo'.
Forma amalgamada de la preposición con y el segmento pronominal migo.
- pron. person. 1.ª pers. m. y f. sing. Con la persona que habla o escribe. Puedes contar conmigo.
"Escápate" is the imperative form for the 2nd person singular form of the verb "escapar]2" (to run away, to escape). Well, the form is actually "escapa", but in this case, is used as a pronominal verb and needs the "te" pronoun meaning "you".
So basically, it means "escape with me" but depending on the context, could mean something slightly different or with different connotations, like "run away with me", "let's elope" or "get away with me", "come away with me", etc.
Notice that it could not mean "escape from me". In Spanish that would be "escapa de mí" and not "escapa conmigo" (with me).