Barcelona Airport has two left luggage offices. One is in terminal T1 and other in terminal T2B hall, although the latter will no longer provide service, and currently only operational to collect items deposited earlier.
It is a payment service and you will have to choose among three types of lockers, according to the size of the luggage which you want to leave. The prices are the following ones:
Small (35cm x 80cm x 45cm) 3,80 € day (24 horas) or fraction.
Medium (35cm x 80cm x 60cm) 4,40 € day (24 horas) or fraction.
Big (50cm x 80cm x 90cm) 4,90 € day (24 horas) or fraction.
If you need to travel with a very big or voluminous object, and you want to leave something several weeks, there is the storehouse service at Barcelona Airport. This service cost 1,97 €/ day, but you have to pay first the transfer from the left luggage office to the storehouse 39,34 €.
Other economic option is rent a mini storage room in Barcelona for days or weeks.