'Depuis' is used in French to express a duration, in a similar way to 'since' and 'for' in English.
The first and most typical use of 'depuis' is to express an action which began in the past, which is continuing in the present. The verb of a phrase that uses 'depuis' in this sense, will always be conjugated in the present. For example, if you wanted to say 'I have been studying English for 5 years', in French, you would say, 'J'étudie l'anglais depuis cinq ans.'
The second use of 'depuis' is to express an action which began in the past but has since been completed or interrupted, and which is therefore no longer continuing in the present. When using 'depuis' in this way, the verb of the phrase will always be conjugated in either the passé composé or the imparfait. For example, to say that 'I had been living in England for 3 years when my daughter was born', you would say 'Je vivais en Angleterre depuis trois ans quand ma fille est née.'