Watch for cheap imports from China. These are ubiquitous all over Europe these days. As recommended above (point 3), check for quality, Hey, note though this is not to say all leather products coming from China are c*ap, and equally, not all local manufacturers have quality products either. Be smart and check details for quality.
Important, point 5, firstly these are all knockoffs, and, secondiy, current City Hall regulations include fines for both street sellers of counterfeit goods but also buyers (50€).
Besides large shops that you'll find across the city and in which you can find fine leather goods, from Misako to Bosanova to El Corte Inglés among others, there are also several small artisan shops scattered (mostly) in Ciutat Vella and Gracia districts. You need to walk those areas and you'll eventually stumble upon them, many are in unassuming street holes :) (=very small shops). Note some artisans don't have a street shop, they work from their workshops and sell their products either on travelling street markets or online. Also, in smaller towns you'd still find some ol'fashion artisan workshops, but not in the City anymore.
In Barcelona, some artisans you might want to have a look at: